Tag Archives: Mathematical Physics

Boundary dynamics in gravitational theories [CL]

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http://arxiv.org/abs/1811.03688


In this work we critically review the boundary conditions and dynamics of 4D gravitational theories. A general coordinate transformation introduces a new foliation and changes the hypersurface on which a natural boundary condition is imposed; in this sense gauge transformations must be viewed as changing the boundary conditions. This raises the need for an enlarged Hilbert space so as to include the states satisfying different boundary conditions. Through the systematical reduction procedure we obtain the 3D Lagrangian that describes the dynamics of the physical states. We examine the new insights offered by the 3D Lagrangian on BMS-type symmetry and black hole information. In particular we confirm that the boundary dynamics is an indispensable part of the system information.

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I. Park
Mon, 12 Nov 18
6/68

Comments: 35 pages

Statistics of Peaks in Chi-Squared Fields [CL]

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http://arxiv.org/abs/1810.02078


Chi-squared random fields arise naturally from the study of fluctuations in field theories with SO(n) symmetry. The extrema of chi-squared fields are of particular physical interest. In this paper, we undertake a statistical analysis of the stationary points of chi-squared fields, with particular emphasis on extrema. We begin by describing the neighborhood of a stationary point in terms of a biased chi-squared random field, and then compute the expected profile of this field, as well as a variety of associated statistics. We are interested in understanding how spherically symmetric the neighborhood of a stationary point is, on average. To this end, we decompose the biased field into its spherical harmonic modes about this point, and explore their statistics. Using these mode statistics, we construct a metric to gauge the degree of spherical symmetry of the field in this neighborhood. Finally, we show how to leverage the harmonic decomposition to efficiently sample both Gaussian and chi-squared fields about a stationary point.

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J. Bloomfield, S. Face, A. Guth, et. al.
Fri, 5 Oct 18
41/53

Comments: 38 pages + 11 pages of appendices, 5 figures

Generalised model-independent characterisation of strong gravitational lenses IV: formalism-intrinsic degeneracies [CEA]

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http://arxiv.org/abs/1809.03505


Based on the standard gravitational lensing formalism with its effective, projected lensing potential in a given background cosmology, we investigate under which transformations of the source position and of the deflection angle the observable properties of the multiple images, i.e. the time delay differences, the relative image positions, relative shapes, and magnification ratios, remain invariant. As these observables only constrain local lens properties, we derive general, local invariance transformations in the areas covered by the multiple images. We show that the known global invariance transformations, e.g. the mass sheet transformation or the source position transformation, are contained in our invariance transformations, when they are restricted to the areas covered by the multiple images and when lens-model-based degeneracies are ignored, like the freedom to add or subtract masses in unconstrained regions without multiple images. Hence, we have identified the general class of invariance transformations that can occur, in particular in our model-independent local characterisation of strong gravitational lenses.

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J. Wagner
Wed, 12 Sep 18
36/73

Comments: 9 pages, 4 figures, submitted to A&A, comments very welcome

Black hole evaporation in conformal gravity [CL]

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http://arxiv.org/abs/1611.05582


We study the formation and the evaporation of a spherically symmetric black hole in conformal gravity. From the collapse of a spherically symmetric thin shell of radiation, we find a singularity-free non-rotating black hole. This black hole has the same Hawking temperature as a Schwarzschild black hole with the same mass, and it completely evaporates either in a finite or in an infinite time, depending on the ensemble. We consider the analysis both in the canonical and in the micro-canonical statistical ensembles. Last, we discuss the corresponding Penrose diagram of this physical process.

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C. Bambi, L. Modesto, S. Porey, et. al.
Mon, 3 Sep 18
16/54

Comments: 1+13 pages, 3 figures. v2: refereed version

Finite conformal quantum gravity and spacetime singularities [CL]

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http://arxiv.org/abs/1801.03193


We show that a class of finite quantum non-local gravitational theories is conformally invariant at classical as well as at quantum level. This is actually a range of conformal anomaly-free theories in the spontaneously broken phase of the Weyl symmetry. At classical level we show how the Weyl conformal invariance is able to tame all the spacetime singularities that plague not only Einstein gravity, but also local and weakly non-local higher derivative theories. The latter statement is proved by a singularity theorem that applies to a large class of weakly non-local theories. Therefore, we are entitled to look for a solution of the spacetime singularity puzzle in a missed symmetry of nature, namely the Weyl conformal symmetry. Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free black hole exact solutions in a class of conformally invariant theories.

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L. Modesto and L. Rachwal
Mon, 3 Sep 18
23/54

Comments: 6 pages, submitted to the Proceedings of the 3rd Karl Schwarzschild Meeting – Gravity and the Gauge/Gravity Correspondence

Formation and evaporation of an electrically charged black hole in conformal gravity [CL]

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http://arxiv.org/abs/1711.04575


Extending previous work on the formation and the evaporation of black holes in conformal gravity, in the present paper we study the gravitational collapse of a spherically symmetric and electrically charged thin shell of radiation. The process creates a singularity-free black hole. Assuming that in the evaporation process the charge $Q$ is constant, the final product of the evaporation is an extremal remnant with $M=Q$, which is reached in an infinite amount of time. We also discuss the issue of singularity and thermodynamics of black holes in Weyl’s conformal gravity.

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C. Bambi, L. Modesto, S. Porey, et. al.
Mon, 3 Sep 18
45/54

Comments: 8 pages, no figures. v2: refereed version

Black hole evaporation in conformal gravity [CL]

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http://arxiv.org/abs/1611.05582


We study the formation and the evaporation of a spherically symmetric black hole in conformal gravity. From the collapse of a spherically symmetric thin shell of radiation, we find a singularity-free non-rotating black hole. This black hole has the same Hawking temperature as a Schwarzschild black hole with the same mass, and it completely evaporates either in a finite or in an infinite time, depending on the ensemble. We consider the analysis both in the canonical and in the micro-canonical statistical ensembles. Last, we discuss the corresponding Penrose diagram of this physical process.

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C. Bambi, L. Modesto, S. Porey, et. al.
Mon, 3 Sep 18
2/54

Comments: 1+13 pages, 3 figures. v2: refereed version

Finite conformal quantum gravity and spacetime singularities [CL]

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http://arxiv.org/abs/1801.03193


We show that a class of finite quantum non-local gravitational theories is conformally invariant at classical as well as at quantum level. This is actually a range of conformal anomaly-free theories in the spontaneously broken phase of the Weyl symmetry. At classical level we show how the Weyl conformal invariance is able to tame all the spacetime singularities that plague not only Einstein gravity, but also local and weakly non-local higher derivative theories. The latter statement is proved by a singularity theorem that applies to a large class of weakly non-local theories. Therefore, we are entitled to look for a solution of the spacetime singularity puzzle in a missed symmetry of nature, namely the Weyl conformal symmetry. Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free black hole exact solutions in a class of conformally invariant theories.

Read this paper on arXiv…

L. Modesto and L. Rachwal
Mon, 3 Sep 18
7/54

Comments: 6 pages, submitted to the Proceedings of the 3rd Karl Schwarzschild Meeting – Gravity and the Gauge/Gravity Correspondence

Formation and evaporation of an electrically charged black hole in conformal gravity [CL]

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http://arxiv.org/abs/1711.04575


Extending previous work on the formation and the evaporation of black holes in conformal gravity, in the present paper we study the gravitational collapse of a spherically symmetric and electrically charged thin shell of radiation. The process creates a singularity-free black hole. Assuming that in the evaporation process the charge $Q$ is constant, the final product of the evaporation is an extremal remnant with $M=Q$, which is reached in an infinite amount of time. We also discuss the issue of singularity and thermodynamics of black holes in Weyl’s conformal gravity.

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C. Bambi, L. Modesto, S. Porey, et. al.
Mon, 3 Sep 18
22/54

Comments: 8 pages, no figures. v2: refereed version

Constraints Between Equations of State and Mass-Radius Relationships in General Clusters of Stellar Systems [CL]

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http://arxiv.org/abs/1808.09306


In this article we prove three obstruction results on the existence of equations of state in clusters of stellar systems fulfilling mass-radius relationships and some additional bound (on the mass, on the radius or a causal bound). The theorems are proved in large generality. We start with a motivating example of TOV systems and we close by applying our results in stellar systems arising from experimental data.

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Y. Martins, D. Teixeira, L. Campos, et. al.
Wed, 29 Aug 18
31/50

Comments: N/A

Axisymmetric, Rotating and Stratified Star [SSA]

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http://arxiv.org/abs/1807.06482


The paper considers Euler-Poisson equations which govern the steady state of a self gravitating, rotating, axi-symmetric stars under the additional assumption that it is composed of incompressible stratified fluid. The original system of six nonlinear equations is reduced to two equations, one for the mass density and the other for gravitational field. This reduction is carried out separately in cylindrical and spherical coordinates. As a “byproduct” we derive also expressions for the pressure. The resulting equations are then solved approximately and these analytic solutions are used then to determine the shape of the rotating star.

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M. Humi
Wed, 18 Jul 18
36/90

Comments: preprint. ALL comments or feedback will be appreciated

Element history of the Laplace resonance: a dynamical approach [EPA]

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http://arxiv.org/abs/1807.02516


We consider the three-body mean motion resonance defined by the Jovian moons Io, Europa, and Ganymede, which is commonly known as the Laplace resonance. In particular, we construct approximate models for the evolution of the librating argument over the period of 100 years, focusing on its principal amplitude and frequency, and on the observed mean motion combinations associated with the quasi-resonant interactions. First, we numerically propagated the Cartesian equations of motion of the Jovian system for the period under examination, and by comparing the results with a suitable set of ephemerides, we derived the main dynamical effects on the target quantities. Using these effects, we built an alternative Hamiltonian formulation and used the normal forms theory to locate the resonance and to compute its main amplitude and frequency. From the Cartesian model we observe that on the timescale considered and with ephemerides as initial conditions, both the librating argument and the diagnostics are well approximated by considering the mutual gravitational interactions of Jupiter and the Galilean moons (including Callisto), and the effect of Jupiter’s J2 harmonic. Under the same initial conditions, the Hamiltonian formulation in which Callisto and J2 are reduced to their secular contributions achieves larger errors for the quantities above, particularly for the librating argument. By introducing appropriate resonant variables, we show that these errors can be reduced by moving in a certain action-angle phase plane, which in turn implies the necessity of a tradeoff in the selection of the initial conditions. In addition to being a good starting point for a deeper understanding of the Laplace resonance, the models and methods described are easily generalizable to different types of multi-body mean motion resonances. They are also prime tools for studying the dynamics of extrasolar systems.

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F. Paita, A. Celletti and G. Pucacco
Tue, 10 Jul 18
74/79

Comments: 13 pages, 11 Figures, to appear on Astronomy and Astrophysics

Stationary double black hole without naked ring singularity [CL]

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http://arxiv.org/abs/1806.11193


Recently double black hole vacuum and electrovacuum metrics attracted attention as exact solutions suitable for visualization of ultra-compact objects beyond the Kerr paradigm. However, many of the proposed systems are plagued with ring curvature singularities. Here we present a new simple solution of this type which is asymptotically Kerr, has zero electric and magnetic charges, but is endowed with magnetic dipole moment and electric quadrupole moment. It is manifestly free of ring singularities, and contains only a mild string-like singularity on the axis corresponding to a distributional energy-momentum tensor.Its main constituents are two extreme co-rotating black holes carrying equal electric andopposite magnetic and NUT charges.

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G. Clément and D. Gal’tsov
Mon, 2 Jul 18
11/70

Comments: 35 pages revtex4, 8 figures

On the co-orbital motion in Three-Body Problem: Existence of quasi-periodic Horseshoe-shaped orbits [CL]

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http://arxiv.org/abs/1806.07262


Janus and Epimetheus are two co-orbital moons of Saturn (the co-orbital motion is associated with trajectories in 1:1 mean-motion resonance) which exhibit a peculiar dynamics associated with horseshoe-shaped trajectories. As they orbit Saturn on quasi-coplanar and quasi-circular trajectories whose radii are only 50 km apart (less than their respective diameters), every four years the bodies are getting closer and their mutual gravitational influence leads to a swapping of the orbits. The outer moon becoming the inner one and vice-versa, this behavior generates horseshoe-shaped trajectories depicted in an adequate rotating frame.
In spite of analytical theories developed to describe their long-term dynamics as well as the indications provided by some numerical investigations, so far no rigorous long time stability results have been obtained even in the restricted three-body problem.
Following the idea of Arnol’d (1963) (but in a much more tricky context as it is 1:1-resonant, while Arnol’d situation relies on non-resonant Kepler orbits), we provide a rigorous proof of the existence of 2 dimensional-elliptic invariant tori associated with the Janus and Epimetheus horseshoe motion in the planar three-body problem using KAM theory.

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L. Niederman, A. Pousse and P. Robutel
Wed, 20 Jun 18
18/58

Comments: 40 pages, 5 figures

On the impossibility of Dipole Modulation in E and B Mode Polarization Fields of CMB [CEA]

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http://arxiv.org/abs/1806.06325


Cosmic Microwave Background Radiation is characterized by T, Q and U fields. A dipole modulation in these fields has been studied in different contexts. E and B are derived from Q and U fields with the help of the so-called `edth’ operator. In this short write-up, I do a systematic analysis to demonstrate that a dipole modulation in E mode polarization can’t be introduced. Although the analysis has been done for the E mode, a similar exercise can be repeated for B mode as well. It has been explicitly demonstrated that the introduction of a dipole modulation leads to a contradiction and hence such a modulation isn’t allowed.

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R. Kothari
Tue, 19 Jun 18
81/91

Comments: N/A

The wave equation near flat Friedmann-Lemaître-Robertson-Walker and Kasner Big Bang singularities [CL]

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http://arxiv.org/abs/1805.12558


We consider the wave equation, $\square_g\psi=0$, in fixed flat Friedmann-Lema\^itre-Robertson-Walker and Kasner spacetimes with topology $\mathbb{R}_+\times\mathbb{T}^3$. We obtain generic blow up results for solutions to the wave equation towards the Big Bang singularity in both backgrounds. In particular, we characterize open sets of initial data prescribed at a spacelike hypersurface close to the singularity, which give rise to solutions that blow up in an open set of the Big Bang hypersurface ${t=0}$. The initial data sets are characterized by the condition that the Neumann data should dominate, in an appropriate $L^2$-sense, up to two spatial derivatives of the Dirichlet data. For these initial configurations, the $L^2(\mathbb{T}^3)$ norms of the solutions blow up towards the Big Bang hypersurfaces of FLRW and Kasner with inverse polynomial and logarithmic rates respectively. Our method is based on deriving suitably weighted energy estimates in physical space. No symmetries of solutions are assumed.

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G. Fournodavlos, A. Franzen and A. Alho
Fri, 1 Jun 18
49/56

Comments: 14 pages, 1 figure

Isochrony in 3D radial potentials. From Michel Hénon ideas to isochrone relativity: classification, interpretation and applications [CL]

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http://arxiv.org/abs/1804.11282


Revisiting and extending an old idea of Michel H\’enon, we geometrically and algebraically characterize the whole set of isochrone potentials. Such potentials are fundamental in potential theory. They appear in spherically symmetrical systems formed by a large amount of charges (electrical or gravitational) of the same type considered in mean-field theory. Such potentials are defined by the fact that the radial period of a test charge in such potentials, provided that it exists, depends only on its energy and not on its angular momentum.
Our characterization of the isochrone set is based on the action of a real affine subgroup on isochrone potentials related to parabolas in the $\mathbb{R}^2$ plane. Furthermore, any isochrone orbits are mapped onto associated Keplerian elliptic ones by a generalization of the Bohlin transformation. This mapping allows us to understand the isochrony property of a given potential as relative to the reference frame in which its parabola is represented. We detail this isochrone relativity in the special relativity formalism.
We eventually exploit the completeness of our characterization and the relativity of isochrony to propose a deeper understanding of general symmetries such as Kepler’s Third Law and Bertrand’s theorem.

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A. Simon-Petit, J. Perez and G. Duval
Tue, 1 May 18
14/78

Comments: 67 pages, 7 theorems, 6 lemmas, 4 propositions and 2 corrolaries

Revisiting Birkhoff Theorem from a dual null point of view [CL]

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http://arxiv.org/abs/1803.11547


Birkhoff theorem is a well known result in General Relativity and it is used in many applications. However, its most general version, due to Bona, is almost unknown and presented in a form less accessible to the relativists and cosmologists community. Moreover, many wield it mistakenly as a simple transposition of Newton’s iron spheres theorem. In the present work, we propose a modern, dual null, presentation — useful in many explorations, including black holes — of the theorem that renders accessible most of the results of Bona’s version. In addition, we present the most general fluid contents admissible for the application of the theorem, beyond vacuum, and we solve explicitly the corresponding Einstein equations, presenting a family of solutions that share the properties predicted by the Birkhoff theorem.

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A. Maciel, M. Delliou and J. Mimoso
Mon, 2 Apr 18
13/39

Comments: 10 pages, no figures

Maximal extensions and singularities in inflationary spacetimes [CL]

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http://arxiv.org/abs/1803.07085


Extendibility of inflationary spacetimes with flat spatial geometry is investigated. We find that the past boundary of an inflationary spacetime becomes a so-called parallely propagated curvature singularity if the ratio $\dot{H}/a^2$ diverges at the boundary, where $\dot{H}$ and $a$ represent the time derivative of the Hubble parameter and the scale factor, respectively. On the other hand, if the ratio $\dot{H}/a^2$ converges, then the past boundary is regular and continuously extendible. We also develop a method to judge the continuous ($C^0$)extendibility of spacetime in the case of slow-roll inflation driven by a canonical scalar field. As applications of this method, we find that Starobinsky inflation has a $C^0$ parallely propagated curvature singularity, but a small field inflation model with a Higgs-like potential does not. We also find that an inflationary solution in a modified gravity theory with limited curvature invariants is free of such a singularity and is smoothly extendible.

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D. Yoshida and J. Quintin
Wed, 21 Mar 2018
14/61

Comments: 13 pages, 4 figures

Cosmological aspects of the Eisenhart-Duval lift [CL]

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http://arxiv.org/abs/1802.03370


A cosmological extension of the Eisenhart-Duval metric is constructed by incorporating a cosmic scale factor and the energy-momentum tensor into the scheme. The dynamics of the spacetime is governed the Ermakov-Milne-Pinney equation. Killing isometries include spatial translations and rotations, Newton–Hooke boosts and translation in the null direction. Geodesic motion in Ermakov-Milne-Pinney cosmoi is analyzed. The derivation of the Ermakov-Lewis invariant, the Friedmann equations and the Dmitriev-Zel’dovich equations within the Eisenhart–Duval framework is presented.

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M. Cariglia, A. Galajinsky, G. Gibbons, et. al.
Mon, 12 Feb 18
30/53

Comments: 32 pages, 3 figures

Higher-order geometrical optics for circularly-polarized electromagnetic waves [CL]

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http://arxiv.org/abs/1801.02273


We study the geometrical-optics expansion for circularly-polarized electromagnetic waves propagating on a curved spacetime in general relativity. We show that higher-order corrections to the Faraday and stress-energy tensors may be found via a system of transport equations, in principle. At sub-leading order, the stress-energy tensor possesses terms proportional to the wavelength whose sign depends on the handedness of the circular polarization. Due to such terms, the direction of energy flow is not aligned with the gradient of the phase, in general, and the wave may carry a transverse stress. This result appears consistent with the posited existence of an optical Magnus effect, and with a spin-helicity effect in the absorption of electromagnetic waves by a Kerr black hole.

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S. Dolan
Tue, 9 Jan 18
19/94

Comments: 16 pages, no figures

New integrable models and analytical solutions in $f(R)$~cosmology with an ideal gas [CL]

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http://arxiv.org/abs/1801.01274


In the context of $f\left( R\right) $-gravity with a spatially flat FLRW metric containing an ideal fluid, we use the method of invariant transformations to specify families of models which are integrable. We find three families of $f(R)$ theories for which new analytical solutions are given and closed-form solutions are provided.

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G. Papagiannopoulos, S. Basilakos, J. Barrow, et. al.
Mon, 8 Jan 18
97/117

Comments: 14 pages, 2 figures, to appear in Physical Review D

Bianchi cosmologies with $p$-form gauge fields [CL]

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http://arxiv.org/abs/1712.08752


In this paper the dynamics of free gauge fields in Bianchi type I-VII${h}$ space-times is investigated. The general equations for a matter sector consisting of a $p$-form field strength ($p\,\in\,{1,3}$), a cosmological constant ($4$-form) and perfect fluid in Bianchi type I-VII${h}$ space-times are computed using the orthonormal frame method. The number of independent components of a $p$-form in all Bianchi types I-IX are derived and, by means of the dynamical systems approach, the behaviour of such fields in Bianchi type I and V are studied. Both a local and a global analysis are performed and strong global results regarding the general behaviour are obtained. New self-similar cosmological solutions appear both in Bianchi type I and Bianchi type V, in particular, a one-parameter family of self-similar solutions,”Wonderland ($\lambda$)” appears generally in type V and in type I for $\lambda=0$. Depending on the value of the equation of state parameter other new stable solutions are also found (“The Rope” and “The Edge”) containing a purely spatial field strength that rotates relative to the co-moving inertial tetrad. Using monotone functions, global results are given and the conditions under which exact solutions are (global) attractors are found.

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B. Normann, S. Hervik, A. Ricciardone, et. al.
Wed, 27 Dec 2017
7/56

Comments: N/A

Balancing Anisotropic Curvature with Gauge Fields in a Class of Shear-Free Cosmological Models [CL]

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http://arxiv.org/abs/1712.02778


We systematically investigate shear-free cosmological models realized by p-form gauge fields; a scenario in which anisotropic spatial sections expand isotropically with expansion histories equivalent to standard FLRW models. Specifically, we present a complete list of general relativistic shear-free solutions in a class of anisotropic, spatially homogeneous and orthogonal cosmological models containing a collection of $n$ independent $p$-form gauge fields, where $p\in{0,1,2,3}$, in addidtion to standard LCDM matter fields modelled as perfect fluids. Here a (collection of) gauge field(s) balances anisotropic spatial curvature on the right-hand side of the shear propagation equation. The result is a class of solutions dynamically equivalent to standard FLRW cosmologies, with an effective curvature constant $K_\text{eff}$ that depends both on spatial curvature and the energy density of the gauge field(s). In the case of a single gauge field ($n=1$) we show that the only spacetimes that admit such solutions are the LRS Bianchi type III, Bianchi type VI$0$ and Kantowski-Sachs metric, which are dynamically equivalent to open ($K\text{eff}<0$), flat ($K_\text{eff}=0$) and closed ($K_\text{eff}>0$) FLRW models, respectively. With a collection of gauge fields ($n>1$) also Bianchi type II admits a shear-free solution ($K_\text{eff}>0$). We identify the LRS Bianchi type III solution to be the unique shear-free solution with a gauge field Hamiltonian bounded from below in the entire class of models. This is a generalization and unification of the shear-free solutions discovered by Carneiro et. al. (2001) with a massless scalar field and by Koivisto et. al. (2011) with a 2-form gauge field, which we show are physically equivalent at the field strength $p+1$ level. Along the way we develop strategies and a framework that can be utilized in a broader class of models.

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M. Thorsrud
Fri, 8 Dec 17
35/70

Comments: 52 pages, see page 5-7 for summary of main results

Dust fluid component from Lie symmetries in Scalar field Cosmology [CL]

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http://arxiv.org/abs/1710.08666


We show that in scalar-field cosmology, a dust fluid follows as quantum corrections from solutions of the Wheeler-DeWitt equation generated by Lie symmetries. The energy density of the dust fluid is related with the frequency of the wavefunction.

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A. Paliathanasis
Wed, 25 Oct 17
53/68

Comments: 3 pages, to appear in MPLA

Anamorphic Quasiperiodic Universes in Modified and Einstein Gravity with Loop Quantum Gravity Corrections [CL]

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http://arxiv.org/abs/1611.05295


The goal of this work is to elaborate on new geometric methods of constructing exact and parametric quasiperiodic solutions for anamorphic cosmology models in modified gravity theories, MGTs, and general relativity, GR. There exist previously studied generic off-diagonal and diagonalizable cosmological metrics encoding gravitational and matter fields with quasicrystal like structures, QC, and holonomy corrections from loop quantum gravity, LQG. We apply the anholonomic frame deformation method, AFDM, in order to decouple the (modified) gravitational and matter field equations in general form. This allows us to find integral varieties of cosmological solutions determined by generating functions, effective sources, integration functions and constants. The coefficients of metrics and connections for such cosmological configurations depend, in general, on all spacetime coordinates and can be chosen to generate observable (quasi)-periodic/ aperiodic/ fractal / stochastic / (super) cluster / filament / polymer like (continuous, stochastic, fractal and/or discrete structures) in MGTs and/or GR. In this work, we study new classes of solutions for anamorphic cosmology with LQG holonomy corrections. Such solutions are characterized by nonlinear symmetries of generating functions for generic off–diagonal cosmological metrics and generalized connections, with possible nonholonomic constraints to Levi-Civita configurations and diagonalizable metrics depending only on a time like coordinate. We argue that anamorphic quasiperiodic cosmological models integrate the concept of quantum discrete spacetime, with certain gravitational QC-like vacuum and nonvacuum structures. And, that of a contracting universe that homogenizes, isotropizes and flattens without introducing initial conditions or multiverse problems.

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M. Amaral, R. Aschheim, L. Bubuianu, et. al.
Tue, 24 Oct 17
16/68

Comments: latex2e, 11pt, 32 pages, v3 accepted to CQG with a new Appendix and minor modifications following referee’s requests

Recent progress on the description of relativistic spin: vector model of spinning particle and rotating body with gravimagnetic moment in General Relativity [CL]

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http://arxiv.org/abs/1710.07135


We review the recent results on development of vector models of spin and apply them to study the influence of spin-field interaction on the trajectory and precession of a spinning particle in external gravitational and electromagnetic fields. The formalism is developed starting from the Lagrangian variational problem, which implies both equations of motion and constraints which should be presented in a model of spinning particle. We present a detailed analysis of the resulting theory and show that it has reasonable properties on both classical and quantum level. We describe a number of applications and show how the vector model clarifies some issues presented in theoretical description of a relativistic spin: A) One-particle relativistic quantum mechanics with positive energies and its relation with the Dirac equation and with relativistic {\it Zitterbewegung}; B) Spin-induced non commutativity and the problem of covariant formalism; C) Three-dimensional acceleration consistent with coordinate-independence of the speed of light in general relativity and rainbow geometry seen by spinning particle; D) Paradoxical behavior of the Mathisson-Papapetrou-Tulczyjew-Dixon equations of a rotating body in ultra relativistic limit, and equations with improved behavior.

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A. Deriglazov and W. Ramirez
Mon, 23 Oct 17
52/52

Comments: Invited review article for the Journal “Advances in Mathematical Physics”. Based on the recent works: arXiv:1312.6247, arXiv:1406.6715, arXiv:1409.4756, arXiv:1509.05357, arXiv:1511.00645, arXiv:1609.00043. 61 pages, 3 figures

Dynamics of resonances and equilibria of Low Earth Objects [EPA]

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http://arxiv.org/abs/1710.02519


The nearby space surrounding the Earth is densely populated by artificial satellites and instruments, whose orbits are distributed within the Low-Earth-Orbit region (LEO), ranging between 90 and 2 000 $km$ of altitude. As a consequence of collisions and fragmentations, many space debris of different sizes are left in the LEO region. Given the threat raised by the possible damages which a collision of debris can provoke with operational or manned satellites, the study of their dynamics is nowadays mandatory. This work is focused on the existence of equilibria and the dynamics of resonances in LEO. We base our results on a simplified model which includes the geopotential and the atmospheric drag. Using such model, we make a qualitative study of the resonances and the equilibrium positions, including their location and stability. The dissipative effect due to the atmosphere provokes a tidal decay, but we give examples of different behaviors, precisely a straightforward passage through the resonance or rather a temporary capture. We also investigate the effect of the solar cycle which is responsible of fluctuations of the atmospheric density and we analyze the influence of Sun and Moon on LEO objects.

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A. Celletti and C. Gales
Tue, 10 Oct 17
19/70

Comments: 39 pages, 10 figures

Finsler-Randers Cosmology: dynamical analysis and growth of matter perturbations [CL]

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http://arxiv.org/abs/1709.03748


We study for the first time the dynamical properties and the growth index of linear matter perturbations of the Finsler-Randers (FR) cosmological model, for which we consider that the cosmic fluid contains matter, radiation and a scalar field. Initially, for various FR scenarios we implement a critical point analysis and we find solutions which provide cosmic acceleration and under certain circumstances we can have de-Sitter points as stable late-time attractors. Then we derive the growth index of matter fluctuations in various Finsler-Randers cosmologies. Considering cold dark matter and neglecting the scalar field component from the perturbation analysis we find that the asymptotic value of the growth index is $\gamma_{\infty}^{(FR)}\approx\frac {9}{16}$, which is close to that of the concordance $\Lambda$ cosmology, $\gamma^{(\Lambda)} \approx\frac{6}{11}$. In this context, we show that the current FR model provides the same Hubble expansion with that of Dvali, Gabadadze and Porrati (DGP) gravity model. However, the two models can be distinguished at the perturbation level since the growth index of FR model is $\sim18.2\%$ lower than that of the DPG gravity $\gamma^{(DGP)} \approx \frac{11}{16}$. If we allow pressure in the matter fluid then we obtain $\gamma_{\infty}^{(FR)}\approx\frac{9(1+w_{m})(1+2w_{m})}{2[8+3w_{m}% (5+3w_{m})]}$, where $w_{m}$ is the matter equation of state parameter. Finally, we extend the growth index analysis by using the scalar field and we find that the evolution of the growth index in FR cosmologies is affected by the presence of scalar field.

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G. Papagiannopoulos, S. Basilakos, A. Paliathanasis, et. al.
Wed, 13 Sep 17
44/72

Comments: 16 pages, no figures, to be published in Classical and Quantum Gravity

On multiplicative Lie invariants and two-fluid plasma Cauchy invariants equation [CL]

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http://arxiv.org/abs/1709.03356


To understand and model non-ideal flows, we use the simple result $(\partial_t + L_v) (\omega_1 \wedge \omega_2) = S_1 \wedge \omega_2 + \omega_1 \wedge S_2$ from the Lie-varying forms $(\partial_t + L_v) \omega_i = S_i: \ i = 1, 2$. If the (Lie-)sources/sinks satisfy $S_1 \wedge \omega_2 + \omega_1 \wedge S_2 = 0$, a multiplicative' Lie invariant follows, extending the classical approaches offinding new invariants from known ones of ideal flows’ and of modeling non-ideal flows constrained by invariant(s), beyond the traditional ones, the Gauss method, say. Precise relations, such as the generalised Cauchy invariants equation, as found here for two-fluid plasma dynamics, also extend to wider application space.

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J. Zhu
Tue, 12 Sep 17
65/71

Comments: N/A

Cartan symmetries and global dynamical systems analysis in a higher-order modified teleparallel theory [CL]

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http://arxiv.org/abs/1709.02197


In a higher-order modified teleparallel theory cosmological we present analytical cosmological solutions. In particular we determine forms of the unknown potential which drives the scalar field such that the field equations form a Liouville integrable system. For the determination of the conservation laws we apply the Cartan symmetries. Furthermore, inspired from our solutions, a toy model is studied and it is shown that it can describe the Supernova data, while at the same time introduces dark matter components in the Hubble function. When the extra matter source is a stiff fluid then we show how analytical solutions for Bianchi I universes can be constructed from our analysis. Finally, we perform a global dynamical analysis of the field equations by using variables different from that of the Hubble-normalization.

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L. Karpathopoulos, S. Basilakos, G. Leon, et. al.
Fri, 8 Sep 17
3/65

Comments: 47 pages, 5 figures

Causal properties of nonlinear gravitational waves in modified gravity [CL]

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http://arxiv.org/abs/1709.01628


Some exact, nonlinear, vacuum gravitational wave solutions are derived for certain polynomial $f(R)$ gravities. We show that the boundaries of the gravitational domain of dependence, associated with events in polynomial $f(R)$ gravity, are not null as they are in general relativity. The implication is that electromagnetic and gravitational causality separate into distinct notions in modified gravity, which may have observable astrophysical consequences. The linear theory predicts that tachyonic instabilities occur, when the quadratic coefficient $a_{2}$ of the Taylor expansion of $f(R)$ is negative, while the exact, nonlinear, cylindrical wave solutions presented here can be superluminal for all values of $a_{2}$. Anisotropic solutions are found, whose wave-fronts trace out time- or space-like hypersurfaces with complicated geometric properties. We show that the solutions exist in $f(R)$ theories that are consistent with Solar System and pulsar timing experiments.

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A. Suvorov and A. Melatos
Thu, 7 Sep 17
16/65

Comments: 8 pages, 3 figures, 1 table. Accepted for publication in PRD

Light Deflection and Gauss–Bonnet Theorem: Definition of Total Deflection Angle and its Applications [CL]

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http://arxiv.org/abs/1708.04011


In this paper, we re-examine the light deflection in the Schwarzschild and the Schwarzschild–de Sitter spacetime. First, supposing a static and spherically symmetric spacetime, we propose the definition of the total deflection angle $\alpha$ of the light ray by constructing a quadrangle $\Sigma^4$ on the optical reference geometry ${\cal M}^{\rm opt}$ determined by the optical metric $\bar{g}{ij}$. On the basis of the definition of the total deflection angle $\alpha$ and the Gauss–Bonnet theorem, we derive two formulas to calculate the total deflection angle $\alpha$; (1) the angular formula that uses four angles determined on the optical reference geometry ${\cal M}^{\rm opt}$ or the curved $(r, \phi)$ subspace ${\cal M}^{\rm sub}$ being a slice of constant time $t$ and (2) the integral formula on the optical reference geometry ${\cal M}^{\rm opt}$ which is the areal integral of the Gaussian curvature $K$ in the area of a quadrangle $\Sigma^4$ and the line integral of the geodesic curvature $\kappa_g$ along the curve $C{\Gamma}$. The curve $C_{\Gamma}$ is the unperturbed reference straight line that is the geodesic $\Gamma$ on the background spacetime such as the Minkowski or the de Sitter spacetime, and therefore $C_{\Gamma}$ is a straight line in the Euclidean sense. We demonstrate that the two formulas give the same total deflection angle $\alpha$ for the Schwarzschild and the Schwarzschild–de Sitter spacetime. In particular, in the Schwarzschild case, the result coincides with Epstein–Shapiro’s formula when the source $S$ and the receiver $R$ of the light ray are located at infinity. In addition, in the Schwarzschild–de Sitter case, there appear order ${\cal O}(\Lambda m)$ terms in addition to the Schwarzschild-like part, while order ${\cal O}(\Lambda)$ terms disappear.

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H. Arakida
Wed, 16 Aug 17
34/46

Comments: 34 pages, 6 figures. Submitted to PRD

Reviving The Shear-Free Perfect Fluid Conjecture In General Relativity [CL]

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http://arxiv.org/abs/1708.02462


Employing a Mathematica symbolic computer algebra package called xTensor, we present $(1+3)$-covariant special case proofs of the shear-free conjecture for perfect fluids in General Relativity. We first present the case where the pressure is constant and then where the acceleration is parallel to the vorticity vector, which were first presented in their covariant form by Senovilla et. al. We then provide a covariant proof for the case where the acceleration and vorticity vectors are orthogonal, which leads to the existence of a Killing vector along the vorticity. This Killing vector satisfies the new constraint equations resulting from the vanishing of the shear, and it is shown that for the conjecture to be true, this Killing vector must have a vanishing spatially projected directional covariant derivative along the velocity vector field, which in turn implies the existence of another \textit{basic} vector field along the direction of the vorticity for the theorem to hold. Finally, we show that in general if the acceleration is non-zero, there exist a \textit{basic} vector field parallel to the acceleration for the conjecture to be true.

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M. Sikhonde and P. Dunsby
Wed, 9 Aug 17
18/32

Comments: 38 pages, Submitted to CQG

Distribution functions for a family of general-relativistic Hypervirial models in collisionless regime [CL]

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http://arxiv.org/abs/1707.08666


By considering the Einstein-Vlasov system for static spherically symmetric distributions of matter, we show that configurations with constant anisotropy parameter $\beta$ have, necessarily, a distribution function (DF) of the form $F=l^{-2\beta}\xi(\varepsilon)$, where $\varepsilon=E/m$ and $l=L/m$ are the relativistic energy and angular momentum per unit rest mass, respectively. We exploit this result to obtain DFs for the general relativistic extension of the Hypervirial family introduced by Nguyen and Lingam (2013), which Newtonian potential is given by $\phi(r)=-\phi_o /[1+(r/a)^{n}]^{1/n}$ ($a$ and $\phi_o$ are positive free parameters, $n=1,2,…$). Such DFs can be written in the form $F_{n}=l^{n-2}\xi_{n}(\varepsilon)$. For odd $n$, we find that $\xi_n$ is a polynomial of order $2n+1$ in $\varepsilon$, as in the case of the Hernquist model ($n=1$), for which $F_1\propto l^{-1}\left(2\varepsilon-1\right)\left(\varepsilon-1\right)^2$. For even $n$, we can write $\xi_n$ in terms of incomplete beta functions (Plummer model, $n=2$, is an example). Since we demand that $F\geq 0$ throughout the phase space, the particular form of each $\xi_n$ leads to restrictions for the values of $\phi_o$. For example, for the Hernquist model we find that $0\leq \phi_o \leq2/3$, i.e. an upper bounding value less than the one obtained for Nguyen and Lingam ($0\leq \phi_o \leq1$), based on energy conditions.

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H. Gauy and J. Ramos-Caro
Fri, 28 Jul 17
30/48

Comments: N/A

Exact Geodesic Distances in FLRW Spacetimes [CL]

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http://arxiv.org/abs/1705.00730


Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesics distances in an arbitrary spacetime. We show that in spatially flat $(3+1)$-dimensional Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.

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W. Cunningham, D. Rideout, J. Halverson, et. al.
Wed, 3 May 17
7/60

Comments: 11 pages, 2 figures

Travelling waves and a fruitful `time' reparametrization in relativistic electrodynamics [CL]

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http://arxiv.org/abs/1607.03482


We simplify the nonlinear equations of motion of charged particles in an external electromagnetic field that is the sum of a plane travelling wave F_t(ct-z) and a static part F_s(x,y,z): by adopting the light-like coordinate ct-z instead of time t as an independent variable in the Action, Lagrangian and Hamiltonian, and deriving the new Euler-Lagrange and Hamilton equations accordingly, we make the unknown z(t) disappear from the argument of F_t. We study and solve first the single particle equations in few significant cases of extreme accelerations. In particular we obtain a rigorous formulation of a Lawson-Woodward-type (no-final-acceleration) theorem and a compact derivation of cyclotron autoresonance, beside new solutions in the presence of uniform F_s. We then extend our method to plasmas in hydrodynamic conditions and apply it to plane problems: the system of partial differential equations may be partially solved and sometimes even completely reduced to a family of decoupled systems of ordinary ones; this occurs e.g. with the impact of the travelling wave on a vacuum-plasma interface (what may produce the slingshot effect). Since Fourier analysis plays no role in our general framework, the method can be applied to all kind of travelling waves, ranging from almost monochromatic to socalled “impulses”, which contain few, one or even no complete cycle.

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G. Fiore
Fri, 28 Apr 17
3/55

Comments: Latex file, 36 pages, 5 figures

The Memory Effect for Plane Gravitational Waves [CL]

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http://arxiv.org/abs/1704.05997


We give an account of the “gravitational memory effect” in the presence of an exact plane wave solution of Einstein’s vacuum equations. This allows an elementary but exact description of the soft gravitons and how their presence may be detected by observing the motion of freely falling particles.

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P. Zhang, C. Duval, G. Gibbons, et. al.
Mon, 24 Apr 17
8/54

Comments: 7 pages, 2 figures

Cascades and Dissipative Anomalies in Compressible Fluid Turbulence [CL]

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http://arxiv.org/abs/1704.03532


We investigate dissipative anomalies in a turbulent fluid governed by the compressible Navier-Stokes equation. We follow an exact approach pioneered by Onsager, which we explain as a non-perturbative application of the principle of renormalization-group invariance. In the limit of high Reynolds and P\’eclet numbers, the flow realizations are found to be described as distributional or “coarse-grained” solutions of the compressible Euler equations, with standard conservation laws broken by turbulent anomalies. The anomalous dissipation of kinetic energy is shown to be due not only to local cascade, but also to a distinct mechanism called pressure-work defect. Irreversible heating in stationary, planar shocks with an ideal-gas equation of state exemplifies the second mechanism. Entropy conservation anomalies are also found to occur by two mechanisms: an anomalous input of negative entropy (negentropy) by pressure-work and a cascade of negentropy to small scales. We derive “4/5th-law”-type expressions for the anomalies, which allow us to characterize the singularities (structure-function scaling exponents) required to sustain the cascades. We compare our approach with alternative theories and empirical evidence. It is argued that the “Big Power-Law in the Sky” observed in electron density scintillations in the interstellar medium is a manifestation of a forward negentropy cascade, or an inverse cascade of usual thermodynamic entropy.

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G. Eyink and T. Drivas
Thu, 13 Apr 17
1/56

Comments: N/A

Cascades and Dissipative Anomalies in Relativistic Fluid Turbulence [CL]

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http://arxiv.org/abs/1704.03541


We develop first-principles theory of relativistic fluid turbulence at high Reynolds and P\’eclet numbers. We follow an exact approach pioneered by Onsager, which we explain as a non-perturbative application of the principle of renormalization-group invariance. We obtain results very similar to those for non-relativistic turbulence, with hydrodynamic fields in the inertial-range described as distributional or “coarse-grained” solutions of the relativistic Euler equations. These solutions do not, however, satisfy the naive conservation-laws of smooth Euler solutions but are afflicted with dissipative anomalies in the balance equations of internal energy and entropy. The anomalies are shown to be possible by exactly two mechanisms, local cascade and pressure-work defect. We derive “4/5th-law”-type expressions for the anomalies, which allow us to characterize the singularities (structure-function scaling exponents) required for their non-vanishing. We also investigate the Lorentz covariance of the inertial-range fluxes, which we find is broken by our coarse-graining regularization but which is restored in the limit that the regularization is removed, similar to relativistic lattice quantum field theory. In the formal limit as speed of light goes to infinity, we recover the results of previous non-relativistic theory. In particular, anomalous heat input to relativistic internal energy coincides in that limit with anomalous dissipation of non-relativistic kinetic energy.

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G. Eyink and T. Drivas
Thu, 13 Apr 17
24/56

Comments: N/A

Lectures on the Infrared Structure of Gravity and Gauge Theory [CL]

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http://arxiv.org/abs/1703.05448


This is a redacted transcript of a course given by the author at Harvard in spring semester 2016. It contains a pedagogical overview of recent developments connecting the subjects of soft theorems, the memory effect and asymptotic symmetries in four-dimensional QED, nonabelian gauge theory and gravity with applications to black holes. The lectures may be viewed online at https://goo.gl/3DJdOr. Please send typos or corrections to strominger@physics.harvard.edu.

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A. Strominger
Fri, 17 Mar 17
18/50

Comments: 154 pages, 21 figures

Periodic and quasi-periodic attractors for the spin-orbit evolution of Mercury with a realistic tidal torque [CL]

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http://arxiv.org/abs/1703.01189


Mercury is entrapped in a 3:2 resonance: it rotates on its axis three times for every two revolutions it makes around the Sun. It is generally accepted that this is due to the large value of the eccentricity of its orbit. However, the mathematical model originally introduced to study its spin-orbit evolution proved not to be entirely convincing, because of the expression commonly used for the tidal torque. Only recently, in a series of papers mainly by Efroimsky and Makarov, a different model for the tidal torque has been proposed, which has the advantages of being more realistic, and of providing a higher probability of capture in the 3:2 resonance with respect to the previous models. On the other hand, a drawback of the model is that the function describing the tidal torque is not smooth and consists of a superposition of kinks, so that both analytical and numerical computations turn out to be rather delicate: indeed, standard perturbation theory based on power series expansion cannot be applied and the implementation of a fast algorithm to integrate the equations of motion numerically requires a high degree of care. In this paper, we make a detailed study of the spin-orbit dynamics of Mercury, as predicted by the realistic model: In particular, we present numerical and analytical results about the nature of the librations of Mercury’s spin in the 3:2 resonance. The results provide evidence that the librations are quasi-periodic in time.

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M. Bartuccelli, J. Deane and G. Gentile
Mon, 6 Mar 17
38/47

Comments: 32 pages, 8 figures, 5 tables

Dirac-Bergmann Constraints in Physics: Singular Lagrangians, Hamiltonian Constraints and the Second Noether Theorem [CL]

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http://arxiv.org/abs/1702.07598


There is a review of the main mathematical properties of system described by singular Lagrangians and requiring Dirac-Bergmann theory of constraints at the Hamiltonian level. The following aspects are discussed:
i) the connection of the rank and eigenvalues of the Hessian matrix in the Euler-Lagrange equations with the chains of first and second class constraints;
ii) the connection of the Noether identities of the second Noether theorem with the Hamiltonian constraints;
iii) the Shanmugadhasan canonical transformation for the identification of the gauge variables and for the search of the Dirac observables, i.e. the quantities invariant under Hamiltonian gauge transformations.
Review paper for a chapter of a future book.

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L. Lusanna
Mon, 27 Feb 17
23/49

Comments: 38 pages

Dirac-Bergmann Constraints in Relativistic Physics: Non-Inertial Frames, Point Particles, Fields and Gravity [CL]

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http://arxiv.org/abs/1702.07595


There is a review of the physical theories needing Dirac-Bergmann theory of constraints at the Hamiltonian level due to the existence of gauge symmetries. It contains:
i) the treatment of systems of point particles in special relativity both in inertial and non-inertial frames with a Wigner-covariant way of eliminating relative times in relativistic bound states;
ii) the description of the electro-magnetic field in relativistic atomic physics and of Yang-Mills fields in absence of Gribov ambiguity in particle physics;
iii) the identification of the inertial gauge variables and of the physical variables in canonical ADM tetrad gravity in presence of the electro-magnetic field and of charged scalar point particles in asymptotically Minkowskian space-times without super-translations by means of a Shanmugadhasan canonical transformation to a York canonical basis adapted to ten of the 14 first-class constraints and the definition of the Hamiltonian Post-Minkowskian weak field limit.
Review paper for a chapter of a future book

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L. Lusanna
Mon, 27 Feb 17
40/49

Comments: 30 pages. arXiv admin note: substantial text overlap with arXiv:1108.3224, arXiv:1205.2481

Noether symmetries and stability of ideal gas solution in Galileon Cosmology [CL]

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http://arxiv.org/abs/1702.01603


A class of generalized Galileon cosmological models, which can be described by a point-like Lagrangian, is considered in order to utilize Noether’s Theorem to determine conservation laws for the field equations. In the Friedmann-Lema\^{\i}tre-Robertson-Walker universe, the existence of a nontrivial conservation law indicates the integrability of the field equations. Due to the complexity of the latter, we apply the differential invariants approach in order to construct special power-law solutions and study their stability.

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N. Dimakis, A. Giacomini, S. Jamal, et. al.
Tue, 7 Feb 17
31/64

Comments: 13 pages, 4 figures

Inflationary $α$-attractor cosmology: A global dynamical systems perspective [CL]

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http://arxiv.org/abs/1702.00306


We study flat FLRW $\alpha$-attractor $\mathrm{E}$- and $\mathrm{T}$-models by introducing a dynamical systems framework that yields regularized unconstrained field equations on two-dimensional compact state spaces. This results in both illustrative figures and a complete description of the entire solution spaces of these models, including asymptotics. In particular, it is shown that observational viability, which requires a sufficient number of e-folds, is associated with a solution given by a one-dimensional center manifold of a past asymptotic de Sitter state, where the center manifold structure also explains why nearby solutions are attracted to this `inflationary attractor solution.’ A center manifold expansion yields a description of the inflationary regime with arbitrary analytic accuracy, where the slow-roll approximation asymptotically describes the tangency condition of the center manifold at the asymptotic de Sitter state.

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A. Alho and C. Uggla
Thu, 2 Feb 17
10/52

Comments: 15 pages, 11 figures

Exact collisional plasma fluid theories [CL]

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http://arxiv.org/abs/1701.08037


An expansion of the velocity space distribution functions in terms of multi-index Hermite polynomials is carried out to derive a consistent set of collisional fluid equations for plasmas. The velocity-space moments of the often troublesome nonlinear Landau collision operator are evaluated exactly, and to all orders with respect to the expansion. The collisional moments are shown to be generated by applying gradients on two well-known functions, namely the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The expansion can be truncated at arbitrary order with quantifiable error, providing a consistent and systematic alternative to the Chapman-Enskog procedure which, in plasma physics, boils down to the famous Braginskii equations. To illustrate our approach, we provide the collisional ten-moment equations and prove explicitly that the exact, nonlinear expressions for the momentum- and energy-transfer rate satisfy the correct conservation properties.

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D. Pfefferle, E. Hirvijoki and M. Lingam
Mon, 30 Jan 17
37/41

Comments: N/A

Cosmological Evolution and Exact Solutions in a Fourth-order Theory of Gravity [CL]

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http://arxiv.org/abs/1701.04360


A fourth-order theory of gravity is considered which in terms of dynamics has the same degrees of freedom and number of constraints as those of scalar-tensor theories. In addition it admits a canonical point-like Lagrangian description. We study the critical points of the theory and we show that it can describe the matter epoch of the universe and that two accelerated phases can be recovered one of which describes a de Sitter universe. Finally for some models exact solutions are presented.

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A. Paliathanasis
Tue, 17 Jan 17
44/81

Comments: 11 pages, 2 figures

The structure of invariant tori in a 3D galactic potential [CL]

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http://arxiv.org/abs/1009.1993


We study in detail the structure of phase space in the neighborhood of stable periodic orbits in a rotating 3D potential of galactic type. We have used the color and rotation method to investigate the properties of the invariant tori in the 4D spaces of section. We compare our results with those of previous works and we describe the morphology of the rotational, as well as of the tube tori in the 4D space. We find sticky chaotic orbits in the immediate neighborhood of sets of invariant tori surrounding 3D stable periodic orbits. Particularly useful for galactic dynamics is the behavior of chaotic orbits trapped for long time between 4D invariant tori. We find that they support during this time the same structure as the quasi-periodic orbits around the stable periodic orbits, contributing however to a local increase of the dispersion of velocities. Finally we find that the tube tori do not appear in the 3D projections of the spaces of section in the axisymmetric Hamiltonian we examined.

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M. Katsanikas and P. Patsis
Mon, 9 Jan 17
21/52

Comments: 26 pages, 34 figures, accepted for publication in the International Journal of Bifurcation and Chaos

Chains of rotational tori and filamentary structures close to high multiplicity periodic orbits in a 3D galactic potential [CL]

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http://arxiv.org/abs/1103.3981


This paper discusses phase space structures encountered in the neighborhood of periodic orbits with high order multiplicity in a 3D autonomous Hamiltonian system with a potential of galactic type. We consider 4D spaces of section and we use the method of color and rotation [Patsis and Zachilas 1994] in order to visualize them. As examples we use the case of two orbits, one 2-periodic and one 7-periodic. We investigate the structure of multiple tori around them in the 4D surface of section and in addition we study the orbital behavior in the neighborhood of the corresponding simple unstable periodic orbits. By considering initially a few consequents in the neighborhood of the orbits in both cases we find a structure in the space of section, which is in direct correspondence with what is observed in a resonance zone of a 2D autonomous Hamiltonian system. However, in our 3D case we have instead of stability islands rotational tori, while the chaotic zone connecting the points of the unstable periodic orbit is replaced by filaments extending in 4D following a smooth color variation. For more intersections, the consequents of the orbit which started in the neighborhood of the unstable periodic orbit, diffuse in phase space and form a cloud that occupies a large volume surrounding the region containing the rotational tori. In this cloud the colors of the points are mixed. The same structures have been observed in the neighborhood of all m-periodic orbits we have examined in the system. This indicates a generic behavior.

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M. Katsanikas, P. Patsis and A. Pinotsis
Mon, 9 Jan 17
26/52

Comments: 12 pages,22 figures, Accepted for publication in the International Journal of Bifurcation and Chaos

The structure and evolution of confined tori near a Hamiltonian Hopf Bifurcation [CL]

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http://arxiv.org/abs/1012.2463


We study the orbital behavior at the neighborhood of complex unstable periodic orbits in a 3D autonomous Hamiltonian system of galactic type. At a transition of a family of periodic orbits from stability to complex instability (also known as Hamiltonian Hopf Bifurcation) the four eigenvalues of the stable periodic orbits move out of the unit circle. Then the periodic orbits become complex unstable. In this paper we first integrate initial conditions close to the ones of a complex unstable periodic orbit, which is close to the transition point. Then, we plot the consequents of the corresponding orbit in a 4D surface of section. To visualize this surface of section we use the method of color and rotation [Patsis and Zachilas 1994]. We find that the consequents are contained in 2D “confined tori”. Then, we investigate the structure of the phase space in the neighborhood of complex unstable periodic orbits, which are further away from the transition point. In these cases we observe clouds of points in the 4D surfaces of section. The transition between the two types of orbital behavior is abrupt.

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M. Katsanikas, P. Patsis and G. Contopoulos
Mon, 9 Jan 17
42/52

Comments: 10 pages, 14 figures, accepted for publication in the International Journal of Bifurcation and Chaos

Instabilities and stickiness in a 3D rotating galactic potential [CL]

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http://arxiv.org/abs/1201.2108


We study the dynamics in the neighborhood of simple and double unstable periodic orbits in a rotating 3D autonomous Hamiltonian system of galactic type. In order to visualize the four dimensional spaces of section we use the method of color and rotation. We investigate the structure of the invariant manifolds that we found in the neighborhood of simple and double unstable periodic orbits in the 4D spaces of section. We consider orbits in the neighborhood of the families x1v2, belonging to the x1 tree, and the z-axis (the rotational axis of our system). Close to the transition points from stability to simple instability, in the neighborhood of the bifurcated simple unstable x1v2 periodic orbits we encounter the phenomenon of stickiness as the asymptotic curves of the unstable manifold surround regions of the phase space occupied by rotational tori existing in the region. For larger energies, away from the bifurcating point, the consequents of the chaotic orbits form clouds of points with mixing of color in their 4D representations. In the case of double instability, close to x1v2 orbits, we find clouds of points in the four dimensional spaces of section. However, in some cases of double unstable periodic orbits belonging to the z-axis family we can visualize the associated unstable eigensurface. Chaotic orbits close to the periodic orbit remain sticky to this surface for long times (of the order of a Hubble time or more). Among the orbits we studied we found those close to the double unstable orbits of the x1v2 family having the largest diffusion speed.

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M. Katsanikas, P. Patsis and G. Contopoulos
Mon, 9 Jan 17
44/52

Comments: 29pages, 25 figures, accepted for publication in the International Journal of Bifurcation and Chaos

Conservation laws and evolution schemes in geodesic, hydrodynamic and magnetohydrodynamic flows [CL]

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http://arxiv.org/abs/1612.09308


Carter and Lichnerowicz have established that barotropic fluid flows are conformally geodesic and obey Hamilton’s principle. This variational approach can accommodate neutral, or charged and poorly conducting, fluids. We show that, unlike what has been previously thought, this approach can also accommodate perfectly conducting magnetofluids, via the Bekenstein-Oron description of ideal magnetohydrodynamics. When Noether symmetries associated with Killing vectors or tensors are present in geodesic flows, they lead to constants of motion polynomial in the momenta. We generalize these concepts to hydrodynamic flows. Moreover, the Hamiltonian descriptions of ideal magnetohydrodynamics allow one to cast the evolution equations into a hyperbolic form useful for evolving rotating or binary compact objects with magnetic fields in numerical general relativity. Conserved circulation laws, such as those of Kelvin, Alfv\’en and Bekenstein-Oron, emerge simply as special cases of the Poincar\’e-Cartan integral invariant of Hamiltonian systems. We use this approach to obtain an extension of Kelvin’s theorem to baroclinic (non-isentropic) fluids, based on a temperature-dependent time parameter. We further extend this result to perfectly or poorly conducting baroclinic magnetoflows. Finally, in the barotropic case, such magnetoflows are shown to also be geodesic, albeit in a Finsler (rather than Riemann) space.

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C. Markakis, K. Uryu, E. Gourgoulhon, et. al.
Mon, 2 Jan 17
9/45

Comments: 23 pages

Dynamical models and the onset of chaos in space debris [EPA]

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http://arxiv.org/abs/1612.08849


The increasing threat raised by space debris led to the development of different mathematical models and approaches to investigate the dynamics of small particles orbiting around the Earth. Such models and methods strongly depend on the altitude of the objects above Earth’s surface, since the strength of the different forces acting on an Earth orbiting object (geopotential, atmospheric drag, lunar and solar attractions, solar radiation pressure, etc.) varies with the altitude of the debris.
In this review, our focus is on presenting different analytical and numerical approaches employed in modern studies of the space debris problem. We start by considering a model including the geopotential, solar and lunar gravitational forces and the solar radiation pressure. We summarize the equations of motion using different formalisms: Cartesian coordinates, Hamiltonian formulation using Delaunay and epicyclic variables, Milankovitch elements. Some of these methods lead in a straightforward way to the analysis of resonant motions. In particular, we review results found recently about the dynamics near tesseral, secular and semi-secular resonances.
As an application of the above methods, we proceed to analyze a timely subject namely the possible causes for the onset of chaos in space debris dynamics. Precisely, we discuss the phenomenon of overlapping of resonances, the effect of a large area-to-mass ratio, the influence of lunisolar secular resonances.
We conclude with a short discussion about the effect of the dissipation due to the atmospheric drag and we provide a list of minor effects, which could influence the dynamics of space debris.

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A. Celletti, C. Efthymiopoulos, F. Gachet, et. al.
Fri, 30 Dec 16
39/64

Comments: 39 pages, 4 figures

Number Density of Peaks in a Chi-Squared Field [CL]

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http://arxiv.org/abs/1612.03890


We investigate the statistics of stationary points in the sum of squares of $N$ Gaussian random fields, which we call a “chi-squared” field. The behavior of such a field at a point is investigated, with particular attention paid to the formation of topological defects. An integral to compute the number density of stationary points at a given field amplitude is constructed. We compute exact expressions for the integral in various limits and provide code to evaluate it numerically in the general case. We investigate the dependence of the number density of stationary points on the field amplitude, number of fields, and power spectrum of the individual Gaussian random fields. This work parallels the work of Bardeen, Bond, Kaiser and Szalay, who investigated the statistics of peaks of Gaussian random fields. A number of results for integrating over matrices are presented in appendices.

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J. Bloomfield, S. Face, A. Guth, et. al.
Tue, 13 Dec 16
49/77

Comments: 18 pages + 11 pages appendices, 3 figures

Spacetime completeness of non-singular black holes in conformal gravity [CL]

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http://arxiv.org/abs/1611.00865


We explicitly prove that the Weyl conformal symmetry solves the black hole singularity problem, otherwise unavoidable in a generally covariant local or non-local gravitational theory. Moreover, we yield explicit examples of local and non-local theories enjoying Weyl and diffeomorphism symmetry (in short co-covariant theories). Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free spherically symmetric and axi-symmetric exact solutions for black hole spacetimes conformally equivalent to the Schwarzschild or the Kerr spacetime. We first check the absence of divergences in the Kretschmann invariant for the rescaled metrics. Afterwords, we show that the new types of black holes are geodesically complete and linked by a Newman-Janis transformation just as in standard general relativity (based on Einstein-Hilbert action). Furthermore, we argue that no massive or massless particles can reach the former Schwarzschild singularity or touch the former Kerr ring singularity in a finite amount of their proper time or of their affine parameter. Finally, we discuss the Raychaudhuri equation in a co-covariant theory and we show that the expansion parameter for congruences of both types of geodesics (for massless and massive particles) never reaches minus infinity. Actually, the null geodesics become parallel at the r=0 point in the Schwarzschild spacetime (the origin) and the focusing of geodesics is avoided. The arguments of regularity of curvature invariants, geodesic completeness, and finiteness of geodesics’ expansion parameter ensure us that we are dealing with singularity-free and geodesically-complete black hole spacetimes.

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C. Bambi, L. Modesto and L. Rachwal
Fri, 4 Nov 16
19/58

Comments: 22 pages, 21 pictures. arXiv admin note: text overlap with arXiv:1605.04173

Initial conditions for cosmological perturbations [CL]

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http://arxiv.org/abs/1610.09424


Penrose proposed that the big bang singularity should be constrained by requiring that the Weyl curvature vanishes there. The idea behind this past hypothesis is attractive because it constrains the initial conditions for the universe in geometric terms and is not confined to a specific early universe paradigm. However, the precise statement of Penrose’s hypothesis is tied to classical space-times and furthermore restricts only the gravitational degrees of freedom. These are encapsulated only in the tensor modes of the commonly used cosmological perturbation theory. Drawing inspiration from the underlying idea, we propose a quantum generalization of Penrose’s hypothesis using the Planck regime in place of the big bang, and simultaneously incorporating tensor as well as scalar modes. Initial conditions selected by this generalization constrain the universe to be as homogeneous and isotropic in the Planck regime \emph{as permitted by the Heisenberg uncertainty relations}.

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A. Ashtekar and B. Gupt
Tue, 1 Nov 16
46/75

Comments: 23 pages, 1 figure

Jacobi stability analysis of scalar field models with minimal coupling to gravity in a cosmological background [CL]

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http://arxiv.org/abs/1609.05636


We perform the study of the stability of the cosmological scalar field models, by using the Jacobi stability analysis, or the Kosambi-Cartan-Chern (KCC) theory. In the KCC approach we describe the time evolution of the scalar field cosmologies in geometric terms, by performing a “second geometrization”, by considering them as paths of a semispray. By introducing a non-linear connection and a Berwald type connection associated to the Friedmann and Klein-Gordon equations, five geometrical invariants can be constructed, with the second invariant giving the Jacobi stability of the cosmological model. We obtain all the relevant geometric quantities, and we formulate the condition of the Jacobi stability for scalar field cosmologies in the second order formalism. As an application of the developed methods we consider the Jacobi stability properties of the scalar fields with exponential and Higgs type potential. We find that the Universe dominated by a scalar field exponential potential is in Jacobi unstable state, while the cosmological evolution in the presence of Higgs fields has alternating stable and unstable phases. By using the standard first order formulation of the cosmological models as dynamical systems we have investigated the stability of the phantom quintessence and tachyonic scalar fields, by lifting the first order system to the tangent bundle. It turns out that in the presence of a power law potential both these models are Jacobi unstable during the entire cosmological evolution.

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B. Danila, T. Harko, M. Mak, et. al.
Tue, 20 Sep 16
15/74

Comments: 24 pages, 14 figures, accepted for publication in Advances in High Energy Physics, special issue “Dark Physics in the Early Universe”

Integrable Cosmological Potentials [CL]

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http://arxiv.org/abs/1608.08511


The problem of classification of the Einstein–Friedman cosmological Hamiltonians $H$ with a single scalar inflaton field $\varphi$ that possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint $H=0$ is considered. Necessary and sufficient conditions for the existence of first, second, and third degree integrals are derived. These conditions have the form of ODEs for the cosmological potential $V(\varphi)$. In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in a parametric form in terms of the associated Legendre functions. Six families of special elementary solutions are described and sporadic superintegrable cases are discussed.

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V. Sokolov and A. Sorin
Wed, 31 Aug 16
47/61

Comments: 24 pages, LaTeX, 2 figures

Electromagnetic 3D subsurface imaging with source sparsity for a synthetic object [IMA]

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http://arxiv.org/abs/1608.06795


This paper concerns electromagnetic 3D subsurface imaging in connection with sparsity of signal sources. We explored an imaging approach that can be implemented in situations that allow obtaining a large amount of data over a surface or a set of orbits but at the same time require sparsity of the signal sources. Characteristic to such a tomography scenario is that it necessitates the inversion technique to be genuinely three-dimensional: For example, slicing is not possible due to the low number of sources. Here, we primarily focused on astrophysical subsurface exploration purposes. As an example target of our numerical experiments we used a synthetic small planetary object containing three inclusions, e.g. voids, of the size of the wavelength. A tetrahedral arrangement of source positions was used, it being the simplest symmetric point configuration in 3D. Our results suggest that somewhat reliable inversion results can be produced within the present a priori assumptions, if the data can be recorded at a specific resolution. This is valuable early-stage knowledge especially for design of future planetary missions in which the payload needs to be minimized, and potentially also for the development of other lightweight subsurface inspection systems.

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S. Pursiainen and M. Kaasalainen
Thu, 25 Aug 16
13/43

Comments: 17 pages, 5 figures. This is an author-created, un-copyedited version of an article accepted for publication/published in Inverse Problems. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at this http URL

Ernst formulation of axisymmetric fields in $f(R)$ gravity: applications to neutron stars and gravitational waves [CL]

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http://arxiv.org/abs/1608.03021


The Ernst formulation of the Einstein equations is generalised to accommodate $f(R)$ theories of gravity. It is shown that, as in general relativity, the axisymmetric $f(R)$ field equations for a vacuum spacetime that is either stationary or cylindrically symmetric reduce to a single, non-linear differential equation for a complex-valued scalar function. As a worked example, we apply the generalised Ernst equations to derive a $f(R)$ generalisation of the Zipoy-Voorhees metric, which may be used to describe the gravitational field outside of an ellipsoidal neutron star. We also apply the theory to investigate the phase speed of large-amplitude gravitational waves in $f(R)$ gravity in the context of soliton-like solutions that display shock-wave behaviour across the causal boundary.

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A. Suvorov and A. Melatos
Thu, 11 Aug 16
47/51

Comments: 12 pages, zero figures. Accepted for publication in PRD

Exact power series solutions of the structure equations of the general relativistic isotropic fluid stars with linear barotropic and polytropic equations of state [CL]

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http://arxiv.org/abs/1607.06877


Obtaining exact solutions of the spherically symmetric general relativistic gravitational field equations describing the interior structure of an isotropic fluid sphere is a long standing problem in theoretical and mathematical physics. The usual approach to this problem consists mainly in the numerical investigation of the Tolman-Oppenheimer-Volkoff and of the mass continuity equations, which describes the hydrostatic stability of the dense stars. In the present paper we introduce an alternative approach for the study of the relativistic fluid sphere, based on the relativistic mass equation, obtained by eliminating the energy density in the Tolman-Oppenheimer-Volkoff equation. Despite its apparent complexity, the relativistic mass equation can be solved exactly by using a power series representation for the mass, and the Cauchy convolution for infinite power series. We obtain exact series solutions for general relativistic dense astrophysical objects described by the linear barotropic and the polytropic equations of state, respectively. For the polytropic case we obtain the exact power series solution corresponding to arbitrary values of the polytropic index $n$. The explicit form of the solution is presented for the polytropic index $n=1$, and for the indexes $n=1/2$ and $n=1/5$, respectively. The case of $n=3$ is also considered. In each case the exact power series solution is compared with the exact numerical solutions, which are reproduced by the power series solutions truncated to seven terms only. The power series representations of the geometric and physical properties of the linear barotropic and polytropic stars are also obtained.

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T. Harko and M. Mak
Tue, 26 Jul 16
75/75

Comments: 21 pages, 3 figures, accepted for publication in Astrophys. Space Science

On dynamical systems approaches and methods in $f(R)$ cosmology [CL]

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http://arxiv.org/abs/1607.05715


We discuss dynamical systems approaches and methods applied to flat Robertson-Walker models in $f(R)$-gravity. We argue that a complete description of the solution space of a model requires a global state space analysis that motivates globally covering state space adapted variables. This is shown explicitly by an illustrative example, $f(R) = R + \alpha R^2$, $\alpha > 0$, for which we introduce new regular dynamical systems on global compactly extended state spaces for the Jordan and Einstein frames. This example also allows us to illustrate several local and global dynamical systems techniques involving, e.g., blow ups of nilpotent fixed points, center manifold analysis, averaging, and use of monotone functions. As a result of applying dynamical systems methods to globally state space adapted dynamical systems formulations, we obtain pictures of the entire solution spaces in both the Jordan and the Einstein frames. This shows, e.g., that due to the domain of the conformal transformation between the Jordan and Einstein frames, not all the solutions in the Jordan frame are completely contained in the Einstein frame. We also make comparisons with previous dynamical systems approaches to $f(R)$ cosmology and discuss their advantages and disadvantages.

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A. Alho, S. Carloni and C. Uggla
Wed, 20 Jul 16
4/66

Comments: 36 pages, 7 figures

Hot dense magnetized ultrarelativistic spinor matter in a slab [CL]

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http://arxiv.org/abs/1606.08241


Properties of hot dense ultrarelativistic spinor matter in a slab of finite width, placed in a transverse uniform magnetic field, are studied. The admissible set of boundary conditions is determined by the requirement that spinor matter be confined inside the slab. In thermal equilibrium, the chiral separation effect in the slab is shown to depend both on temperature and chemical potential; this is distinct from the unrealistic case of the magnetic field filling the unbounded (infinite) medium, when the effect is temperature-independent. In the realistic case of the slab, a stepwise behaviour of the axial current density at zero temperature is smoothed out as temperature increases, turning into a linear behaviour at infinitely large temperature. A choice of boundary conditions can facilitate either augmentation or attenuation of the chiral separation effect; in particular, the effect can persist even at zero chemical potential, if temperature is nonzero. Thus the boundary condition can serve as a source that is additional to the spinor matter density.

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Y. Sitenko
Tue, 28 Jun 16
32/58

Comments: 27 pages, 5 figures. arXiv admin note: text overlap with arXiv:1603.09268

Force-Free Foliations [CL]

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http://arxiv.org/abs/1606.06727


Electromagnetic field configurations with vanishing Lorentz force density are known as force-free and appear in terrestrial, space, and astrophysical plasmas. We explore a general method for finding such configurations based on formulating equations for the field lines rather than the field itself. The basic object becomes a foliation of spacetime or, in the stationary axisymmetric case, of the half-plane. We use this approach to find some new stationary and axisymmetric solutions, one of which could represent a rotating plasma vortex near a magnetic null point.

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G. Compere, S. Gralla and A. Lupsasca
Wed, 22 Jun 16
38/50

Comments: 26 pages, 1 figure

Analytical theory for highly elliptical orbits including time-dependent perturbations [EPA]

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http://arxiv.org/abs/1606.03716


Traditional analytical theories of celestial mechanics are not well-adapted when dealing with highly elliptical orbits. On the one hand, analytical solutions are quite generally expanded into power series of the eccentricity and so limited to quasi-circular orbits. On the other hand, the time-dependency due to the motion of the third body (e.g. Moon and Sun) is almost always neglected. We propose several tools to overcome these limitations. Firstly, we have expanded the third-body disturbing function into a finite polynomial using Fourier series in multiple of the satellite’s eccentric anomaly (instead of the mean anomaly) and involving Hansen-like coefficients. Next, by combining the classical Brouwer-von Zeipel procedure and the time-dependent Lie-Deprit transforms, we have performed a normalization of the expanded Hamiltonian in order to eliminate all the periodic terms. One of the benefits is that the original Brouwer solution for J2 is not modified. The main difficulty lies in the fact that the generating functions of the transformation must be computed by solving a partial differential equation, involving derivatives with respect to the mean anomaly, which appears implicitly in the perturbation. We present a method to solve this equation by means of an iterative process. Finally we have obtained an analytical tool useful for the mission analysis, allowing to propagate the osculating motion of objects on highly elliptical orbits (e>0.6) over long periods efficiently with very high accuracy, or to determine initial elements or mean elements. Comparisons between the complete solution and the numerical simulations will be presented.

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G. Lion and G. Metris
Tue, 14 Jun 16
9/67

Comments: To be submitted soon. Comments are welcome !

Towards an analytical theory of the third-body problem for highly elliptical orbits [EPA]

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http://arxiv.org/abs/1605.07901


When dealing with satellites orbiting a central body on a highly elliptical orbit, it is necessary to consider the effect of gravitational perturbations due to external bodies. Indeed, these perturbations can become very important as soon as the altitude of the satellite becomes high, which is the case around the apocentre of this type of orbit. For several reasons, the traditional tools of celestial mechanics are not well adapted to the particular dynamic of highly elliptical orbits. On the one hand, analytical solutions are quite generally expanded into power series of the eccentricity and therefore limited to quasi-circular orbits [17, 25]. On the other hand, the time-dependency due to the motion of the third-body is often neglected. We propose several tools to overcome these limitations. Firstly, we have expanded the disturbing function into a finite polynomial using Fourier expansions of elliptic motion functions in multiple of the satellite’s eccentric anomaly (instead of the mean anomaly) and involving Hansen-like coefficients. Next, we show how to perform a normalization of the expanded Hamiltonian by means of a time-dependent Lie transformation which aims to eliminate periodic terms. The difficulty lies in the fact that the generator of the transformation must be computed by solving a partial differential equation involving variables which are linear with time and the eccentric anomaly which is not time linear. We propose to solve this equation by means of an iterative process.

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G. Lion, G. Metris and F. Deleflie
Thu, 26 May 16
5/53

Comments: Proceedings of the International Symposium on Orbit Propagation and Determination – Challenges for Orbit Determination and the Dynamics of Artificial Celestial Bodies and Space Debris, Lille, France, 2011

Finite Conformal Quantum Gravity and Nonsingular Spacetimes [CL]

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http://arxiv.org/abs/1605.04173


We explicitly prove that a class of finite quantum gravitational theories (in odd as well as in even dimension) is actually a range of anomaly-free conformally invariant theories in the spontaneously broken phase of the conformal Weyl symmetry. At classical level we show how the Weyl conformal invariance is likely able to tame the spacetime singularities that plague not only Einstein gravity, but also local and weakly non-local higher derivative theories. This latter statement is rigorously proved by a singularity theorem that applies to a large class of weakly non-local theories. Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free black hole exact solutions conformally equivalent to the Schwarzschild metric. Furthermore, we show that the FRW cosmological solutions and the Belinski, Khalatnikov, Lifshitz (BKL) spacetimes, which exactly solve the classical equations of motion, are conformally equivalent to regular spacetimes. Finally, we prove that the Oppenheimer-Volkov gravitational collapse is a an exact (singularity-free) solution of the non-local conformally invariant theory compatible with the bounce paradigm.

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L. Modesto and L. Rachwal
Mon, 16 May 16
4/48

Comments: 34 pages, 8 figures

Symmetry Reduced Loop Quantum Gravity: A Bird's Eye View [CL]

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http://arxiv.org/abs/1605.02648


This is a brief overview of the current status of symmetry reduced models in Loop Quantum Gravity. The goal is to provide an introduction to other more specialized and detailed reviews that follow. Since most of this work is motivated by the physics of the very early universe, I will focus primarily on Loop Quantum Cosmology and discuss quantum aspects of black holes only briefly.

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A. Ashtekar
Tue, 10 May 16
6/85

Comments: 25 pages, 2 figures

Supersymmetric Theory of Stochastic ABC Model: A Numerical Study [CL]

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http://arxiv.org/abs/1604.08609


In this paper, we investigate numerically the stochastic ABC model, a toy model in the theory of astrophysical kinematic dynamos, within the recently proposed supersymmetric theory of stochastics (STS). STS characterises stochastic differential equations (SDEs) by the spectrum of the stochastic evolution operator (SEO) on elements of the exterior algebra or differentials forms over the system’s phase space, X. STS can thereby classify SDEs as chaotic or non-chaotic by identifying the phenomenon of stochastic chaos with the spontaneously broken topological supersymmetry that all SDEs possess. We demonstrate the following three properties of the SEO, deduced previously analytically and from physical arguments: the SEO spectra for zeroth and top degree forms never break topological supersymmetry, all SDEs possesses pseudo-time-reversal symmetry, and each de Rahm cohomology class provides one supersymmetric eigenstate. Our results also suggests that the SEO spectra for forms of complementary degrees, i.e., k and dim X -k, may be isospectral.

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I. Ovchinnikov, Y. Sun, T. Ensslin, et. al.
Mon, 2 May 16
39/49

Comments: Revtex 4-1, 9 pages, 3 figures

Stability and chaos in Kustaanheimo-Stiefel space induced by the Hopf fibration [CL]

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http://arxiv.org/abs/1604.06673


The need for the extra dimension in Kustaanheimo-Stiefel (KS) regularization is explained by the topology of the Hopf fibration, which defines the geometry and structure of KS space. A trajectory in Cartesian space is represented by a four-dimensional manifold, called the fundamental manifold. Based on geometric and topological aspects classical concepts of stability are translated to KS language. The separation between manifolds of solutions generalizes the concept of Lyapunov stability. The dimension-raising nature of the fibration transforms fixed points, limit cycles, attractive sets, and Poincar\’e sections to higher-dimensional subspaces. From these concepts chaotic systems are studied. In strongly perturbed problems the numerical error can break the topological structure of KS space: points in a fiber are no longer transformed to the same point in Cartesian space. An observer in three dimensions will see orbits departing from the same initial conditions but diverging in time. This apparent randomness of the integration can only be understood in four dimensions. The concept of topological stability results in a simple method for estimating the time scale in which numerical simulations can be trusted. Ideally all trajectories departing from the same fiber should be KS transformed to a unique trajectory in three-dimensional space, because the fundamental manifold that they constitute is unique. By monitoring how trajectories departing from one fiber separate from the fundamental manifold a critical time, equivalent to the Lyapunov time, is estimated. These concepts are tested on N-body examples: the Pythagorean problem, and an example of field stars interacting with a binary.

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J. Roa, H. Urrutxua and J. Pelaez
Mon, 25 Apr 16
6/40

Comments: Accepted in MNRAS. 12 pages, 9 figures

Continuum Eigenmodes in Some Linear Stellar Models [CL]

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http://arxiv.org/abs/1603.01875


We apply parallel approaches in the study of continuous spectra to adiabatic stellar models. We seek continuum eigenmodes for the LAWE formulated as both finite difference and linear differential equations. In particular, we apply methods of Jacobi matrices and methods of subordinancy theory in these respective formulations. We find certain pressure-density conditions which admit positive-measured sets of continuous oscillation spectra under plausible conditions on density and pressure. We arrive at results of unbounded oscillations and computational or, perhaps, dynamic instability.

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C. Winfield
Tue, 8 Mar 16
7/83

Comments: N/A

Scalar-tensorial equivalence for higher order $f\left( R,\nabla_μ R,\nabla_{μ_{1}}\nabla_{μ_{2}}R,…,\nabla_{μ_{1}}…\nabla_{μ_{n} }R\right)$ theories of gravity [CL]

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http://arxiv.org/abs/1603.01563


The equivalence between theories depending on the derivatives of $R$, i.e. $f\left( R,\nabla R,…,\nabla^{n}R\right) $, and scalar-tensorial theories is verified. The analysis is done in both metric and Palatini formalisms. It is shown that $f\left( R,\nabla R,…,\nabla^{n}R\right) $ theories are equivalents to Brans-Dicke theories with kinetic terms $\omega_{0}=0$ and $\omega_{0}= – \frac{3}{2}$ for metric and Palatini formalisms respectively. This result is analogous to what happens for $f(R)$ theories. Furthermore, sufficient conditions are established for $f\left( R,\nabla R,…,\nabla^{n}R\right) $ theories to be written as scalar-tensorial theories. Finally, some examples are studied and the comparison of $f\left( R,\nabla R,…,\nabla^{n}R\right) $ theories to $f\left( R,\Box R,…\Box^{n}R\right) $ theories are performed.

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R. Cuzinatto, C. Melo, L. Medeiros, et. al.
Tue, 8 Mar 16
31/83

Comments: 13 pages

Electromagnetic Field in Lyra Manifold: A First Order Approach [CL]

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http://arxiv.org/abs/1603.00853


We discuss the coupling of the electromagnetic field with a curved and torsioned Lyra manifold using the Duffin-Kemmer-Petiau theory. We will show how to obtain the equations of motion and energy-momentum and spin density tensors by means of the Schwinger Variational Principle.

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R. Casana, C. Melo and B. Pimentel
Thu, 3 Mar 16
22/75

Comments: Matches version published ten years ago celebrating 100 years of Relativity. arXiv admin note: substantial text overlap with arXiv:gr-qc/0509117

Oscillating solutions of the Vlasov-Poisson system — A numerical investigation [GA]

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http://arxiv.org/abs/1602.07989


Numerical evidence is given that spherically symmetric perturbations of stable spherically symmetric steady states of the gravitational Vlasov-Poisson system lead to solutions which oscillate in time. The oscillations can be periodic in time or damped. Along one-parameter families of polytropic steady states we establish an Eddington-Ritter type relation which relates the period of the oscillation to the central density of the steady state. The numerically obtained periods are used to estimate possible periods for typical elliptical galaxies.

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T. Ramming and G. Rein
Fri, 26 Feb 16
68/68

Comments: 20 pages

On The Big Bang Singularity in $k=0$ FLRW Cosmologies [CL]

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http://arxiv.org/abs/1602.02456


In this brief paper, we consider the dynamics of a spatially flat FLRW spacetime with a positive cosmological constant and matter obeying a barotropic equation of state. By performing a change of variables on the Raychaudhuri equation, we are able to compactify the big bang singularity to a finite point. We then use Chetaev’s instability theorem to prove that such a model is always past asymptotic to a big bang singularity assuming only the weak energy condition, which is more general than the strong energy condition used in the classical singularity theorems of cosmology.

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I. Kohli
Tue, 9 Feb 16
23/63

Comments: N/A

Geometric dark energy traversable wormholes constrained by astrophysical observations [CL]

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http://arxiv.org/abs/1602.00558


In this letter, we introduce the astrophysical observations into the wormhole research, which is not meant to general parameters constraints for the dark energy models, in order to understand more about in which stage of the universe evolutions wormholes may exist through the investigation of the evolution behavior of the cosmic equation of state parameter. As a concrete instance, we investigate the Ricci dark energy (RDE) traversable wormholes constrained by astrophysical data-sets. Particularly, we can discover from Fig. \ref{fig5} of the present work, when the effective equation of state parameter $\omega_X<-1$, namely, the Null Energy conditions (NEC) is violated clearly, the wormholes will appear (open). Subsequently, six specific solutions of static and spherically symmetric traversable wormhole supported by the RDE are obtained. Except for the case of constant redshift function, in which the solution is not only asymptotically flat but also traversable, the remaining five solutions are all not asymptotically flat, therefore, the exotic matter from the RDE fluids is spatially distributed in the vicinity of the throat. Furthermore, we analyze the physical characteristics and properties of the RDE traversable wormholes. It is worth noting that, through the astrophysical observations, we get constraints on the parameters of RDE model, explore the type of exotic RDE fluids in different stages of the universe changing, limit the number of available models for wormhole research, reduce the number of the wormholes corresponding to different parameters for RDE model and provide a more apparent picture for wormhole investigations from the new perspective of observational cosmology background

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D. Wang and X. Meng
Tue, 2 Feb 16
32/68

Comments: 17ps, 7figs

Concomitant Hamiltonian and topological structures of extended magnetohydrodynamics [CL]

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http://arxiv.org/abs/1602.00128


The paper describes the unique geometric properties of ideal magnetohydrodynamics (MHD), and demonstrates how such features are inherited by extended MHD models, which incorporate two-fluid effects. The helicities and other geometric expressions for these models are presented in a topological context, emphasizing their universal features. Some of the results presented include: the generalized Kelvin circulation theorems, the existence of two Lie-dragged 2-forms, and two concomitant helicities (which can be studied via the Jones polynomial from Chern-Simons theory). The ensuing commonality is traced to the existence of an underlying Hamiltonian structure for all the extended MHD models, exemplified by the presence of a unique noncanonical Poisson bracket, and its associated energy.

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M. Lingam, G. Miloshevich and P. Morrison
Tue, 2 Feb 16
57/68

Comments: 8 pages, 0 figures

Causal Nature and Dynamics of Trapping Horizons in Black Hole Collapse and Cosmology [CL]

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http://arxiv.org/abs/1601.05109


In calculations of gravitational collapse to form black holes, trapping horizons (foliated by marginally trapped surfaces) make their first appearance either within the collapsing matter or where it joins on to a vacuum exterior. Those which then move outwards with respect to the matter have been proposed for use in defining black holes, replacing the global concept of an “event horizon” which has some serious drawbacks for practical applications. We focus here on studying the properties of trapping horizons within spherical symmetry (which gives some simplifications while retaining the most essential general features). Their locations are then given by exactly the same condition ($R=2M$) as for the event horizon in the vacuum Schwarzschild metric, and the same condition also applies for cosmological trapping horizons. We have investigated the causal nature of these horizons (i.e. whether they are spacelike, timelike or null), making contact with the Misner-Sharp formalism, which has often been used for numerical calculations of spherical collapse. We follow two different approaches, one using a geometrical quantity $\alpha$ and the other using the horizon velocity measured with respect to the collapsing (or expanding) matter. Simple expressions are found for each of these in terms of local fluid parameters, and the connection between them allows a full description of the possible behaviours, depending on the initial density profile and the equation of state. After revisiting the FLRW universe model and the pressureless Oppenheimer-Snyder collapse model in the light of this, we have carried out numerical simulations for stellar collapse with non-zero pressure, making contact with pioneering calculations from the 1960s where some features of the emergence and subsequent behaviour of trapping horizons could already be seen.

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A. Helou, I. Musco and J. Miller
Mon, 25 Jan 16
6/56

Comments: 29 pages, 11 figures, to be submitted to Physical Review D

On the astrodynamics applications of Weierstrass elliptic and related functions [EPA]

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http://arxiv.org/abs/1601.04963


Weierstrass elliptic and related functions have been recently shown to enable analytical explicit solutions to classical problems in astrodynamics. These include the constant radial acceleration problem, the Stark problem and the two-fixed center (or Euler’s) problem. In this paper we review the basic technique that allows for these results and we discuss the limits and merits of the approach. Applications to interplanetary trajectory design are then discussed including low-thrust planetary fly-bys and the motion of an artificial satellite under the influence of an oblate primary including $J_2$ and $J_3$ harmonics.

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D. Biscani
Wed, 20 Jan 16
30/58

Comments: Presented at the AAS/AIAA Space Flight Mechanics Meeting, Napa, CA in February 14, 2016

Evolution and Dynamics of a Matter creation model [CL]

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http://arxiv.org/abs/1601.03955


In the flat Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) geometry, we consider the expansion of the universe powered by the gravitationally induced `adiabatic’ matter creation. To demonstrate how matter creation works well with the expanding universe, we have considered a general creation rate and analyzed this rate in the framework of dynamical analysis. The dynamical analysis hints the presence of a non-singular universe (without the big bang singularity) with two successive accelerated phases, one at the very early phase of the universe (i.e., inflation), and the other one describes the current accelerating universe, where this early, late accelerated phases are associated with an unstable fixed point (i.e., repeller) and a stable fixed (attractor) points, respectively. We have described this phenomena by analytic solutions of the Hubble function and the scale factor of the FLRW universe. Using Jacobi Last multiplier method, we have found a Lagrangian for this matter creation rate describing this scenario of the universe. To match with our early physics results, we introduce an equivalent dynamics driven by a single scalar field and discussed the associated observable parameters compared them with the latest PLANCK data sets. Then introducing the teleparallel modified gravity, we have established an equivalent gravitational theory in the framework of matter creation. Further, introducing an equivalence between matter creation and decaying vacuum, we have found an equivalent decaying vacuum model. Finally, we have discussed a model independent test, cosmography, for the present matter creation model.

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S. Pan, J. Haro, A. Paliathanasis, et. al.
Mon, 18 Jan 16
13/50

Comments: 20 pages, No figures, Comments are welcome !

Scale dynamical origin of modification or addition of potential in mechanics. A possible framework for the MOND theory and the dark matter [CL]

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http://arxiv.org/abs/1601.01130


Using our mathematical framework developed in \cite{cresson-pierret_scale} called \emph{scale dynamics}, we propose in this paper a new way of interpreting the problem of adding or modifying potentials in mechanics and specifically in galactic dynamics. An application is done for the two-body problem with a Keplerian potential showing that the velocity of the orbiting body is constant. This would explain the observed phenomenon in the flat rotation curves of galaxies without adding \emph{dark matter} or modifying Newton’s law of dynamics.

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F. Pierret
Thu, 7 Jan 16
35/36

Comments: N/A

On the Hojman conservation quantities in Cosmology [CL]

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http://arxiv.org/abs/1601.00547


We discuss the application of the Hojmans Symmetry Approach for the determination of conservation laws in Cosmology, which has been recently applied by various authors in different cosmological models. We show that Hojman’s method for regular Hamiltonian systems, where the Hamiltonian function is one of the involved equations of the system, is equivalent to the application of Noether’s Theorem for generalized transformations. That means that for minimally-coupled scalar field cosmology or other modified theories which are conformally related with scalar-field cosmology, like $f(R)$ gravity, the application of Hojman’s method provide us with the same results with that of Noether’s theorem. Moreover we study the special Ansatz. $\phi\left( t\right) =\phi\left( a\left( t\right) \right) $, which has been introduced for a minimally-coupled scalar field, and we study the Lie and Noether point symmetries for the reduced equation. We show that under this Ansatz, the unknown function of the model cannot be constrained by the requirement of the existence of a conservation law and that the Hojman conservation quantity which arises for the reduced equation is nothing more than the functional form of the Noether conservation law of momentum for the free particle. On the other hand, for $f(T)$ teleparallel gravity, it is not the existence of Hojman’s conservation laws which provide us with the special function form of $f(T)$ functions, but the requirement that the reduced second-order differential equation admits a Jacobi Last multiplier, while the new conservation law is nothing else that the Hamiltonian function of the reduced equation.

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A. Paliathanasis, P. Leach and S. Capozziello
Tue, 5 Jan 16
64/104

Comments: 5 pages

Closed-form solutions of the Wheeler-DeWitt equation in a scalar-vector field cosmological model by Lie symmetries [CL]

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http://arxiv.org/abs/1512.05434


We apply as selection rule to determine the unknown functions of a cosmological model the existence of Lie point symmetries for the Wheeler-DeWitt equation of quantum gravity. Our cosmological setting consists of a flat Friedmann-Robertson-Walker metric having the scale factor $a(t)$, a scalar field with potential function $V(\phi)$ minimally coupled to gravity and a vector field of its kinetic energy is coupled with the scalar field by a coupling function $f(\phi)$. Then, the Lie symmetries of this dynamical system are investigated by utilizing the behavior of the corresponding minisuperspace under the infinitesimal generator of the desired symmetries. It is shown that by applying the Lie symmetry condition the form of the coupling function and also the scalar field potential function may be explicitly determined so that we are able to solve the Wheeler-DeWitt equation. Finally, we show how we can use the Lie symmetries in order to construct conservation laws and exact solutions for the field equations.

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A. Paliathanasis and B. Vakili
Fri, 18 Dec 15
11/70

Comments: 14 pages, 2 figures; to appear in Gen. Rel. Grav

Testing modified gravity and no-hair relations for the Kerr-Newman metric through quasi-periodic oscillations of galactic microquasars [CL]

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http://arxiv.org/abs/1512.02291


We construct multipole moments for stationary, asymptotically flat, spacetime solutions to higher-order curvature theories of gravity. The moments are defined using $3+1$ techniques involving timelike Killing vector constructions as in the classic papers by Geroch and Hansen. Using the fact that the Kerr-Newman metric is a vacuum solution to a particular class of $f(R)$ theories of gravity, we compute all its moments, and find that they admit recurrence relations similar to those for the Kerr solution in general relativity. It has been proposed previously that modelling the measured frequencies of quasi-periodic oscillations from galactic microquasars enables experimental tests of the no-hair theorem. We explore the possibility that, even if the no-hair relation is found to break down in the context of general relativity, there may be an $f(R)$ counterpart that is preserved. We apply the results to the microquasars GRS $1915$+$105$ and GRO J$1655$-$40$ using the diskoseismology and kinematic resonance models, and constrain the spins and `charges’ [which are not really electric charges in the $f(R)$ context] of their black holes.

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A. Suvorov and A. Melatos
Wed, 9 Dec 15
33/63

Comments: 14 pages, 5 figures; Accepted for publication in PRD

Non-chaotic evolution of triangular configuration due to gravitational radiation reaction in the three-body problem [CL]

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http://arxiv.org/abs/1512.01087


Continuing work initiated in an earlier publication [H. Asada, Phys. Rev. D {\bf 80}, 064021 (2009)], the gravitational radiation reaction to Lagrange’s equilateral triangular solution of the three-body problem is investigated in an analytic method. The previous work is based on the energy balance argument, which is sufficient for a two-body system because the number of degrees of freedom (the semi-major axis and the eccentricity in quasi-Keplerian cases for instance) equals to that of the constants of motion such as the total energy and the orbital angular momentum. In a system with three (or more) bodies, however, the number of degrees of freedom is more than that of the constants of motion. Therefore, the present paper discusses the evolution of the triangular system by directly treating the gravitational radiation reaction force to each body. The perturbed equations of motion are solved by using the Laplace transform technique. It is found that the triangular configuration is adiabatically shrinking and keeps to be in equilibrium with increasing the orbital frequency due to the radiation reaction if the mass ratios satisfy the Newtonian stability condition. Long-term stability involving the first post-Newtonian corrections is also discussed.

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K. Yamada and H. Asada
Fri, 4 Dec 15
45/64

Comments: 17 pages, 1 figures

Derivation of the Hall and Extended Magnetohydrodynamics Brackets [CL]

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http://arxiv.org/abs/1512.00942


There are several plasma models intermediate in complexity between ideal magnetohydrodynamics (MHD) and two-fluid theory, with Hall and Extended MHD being two important examples. In this paper we investigate several aspects of these theories, with the ultimate goal of deriving the noncanonical Poisson brackets used in their Hamiltonian formulations. We present fully Lagrangian actions for each, as opposed to the fully Eulerian, or mixed Eulerian-Lagrangian, actions that have appeared previously. As an important step in this process we exhibit each theory’s two advected fluxes (in analogy to ideal MHD’s advected magnetic flux), discovering also that with the correct choice of gauge they have corresponding Lie-dragged potentials resembling the electromagnetic vector potential, and associated conserved helicities. Finally, using the Euler-Lagrange map, we show how to derive the noncanonical Eulerian brackets from canonical Lagrangian ones.

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E. DAvignon, P. Morrison and M. Lingam
Fri, 4 Dec 15
62/64

Comments: N/A

Bifurcation sequences in the symmetric 1:1 Hamiltonian resonance [CL]

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http://arxiv.org/abs/1512.00707


We present a general review of the bifurcation sequences of periodic orbits in general position of a family of resonant Hamiltonian normal forms with nearly equal unperturbed frequencies, invariant under $Z_2 \times Z_2$ symmetry. The rich structure of these classical systems is investigated with geometric methods and the relation with the singularity theory approach is also highlighted. The geometric approach is the most straightforward way to obtain a general picture of the phase-space dynamics of the family as is defined by a complete subset in the space of control parameters complying with the symmetry constraint. It is shown how to find an energy-momentum map describing the phase space structure of each member of the family, a catastrophe map that captures its global features and formal expressions for action-angle variables. Several examples, mainly taken from astrodynamics, are used as applications.

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A. Marchesiello and G. Pucacco
Thu, 3 Dec 15
65/65

Comments: 36 pages, 10 figures, accepted on International Journal of Bifurcation and Chaos. arXiv admin note: substantial text overlap with arXiv:1401.2855

Quasi-local approach to general universal horizons [CL]

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http://arxiv.org/abs/1511.08663


Theories of gravity with a preferred foliation usually display arbitrarily fast signal propagation, changing the black hole definition. A new inescapable barrier, the universal horizon, has been defined and many static and spherically symmetric examples have been studied in the literature. Here, we translate the usual definition of universal horizon in terms of an optical scalar built with the preferred flow defined by the preferred spacetime foliation. The new expression have the advantage of being of quasi-local nature and not depend on specific spacetime symmetries to be well defined. Therefore, we propose it as a definition for general quasi-local universal horizons. We also to give a general (peeling) surface gravity definition for general spacetimes. Using the new formalism we show that there are no universal analog of cosmological horizons for FLRW models, for any scale factor function and we also state that quasi-local universal horizons are restricted to trapped regions of the spacetime. We analyze the evolution of the universal horizon area under simplifying assumptions and we conclude with our view on the next steps for the understanding of black holes in non relativistic gravity theories.

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A. Maciel
Mon, 30 Nov 15
75/78

Comments: 10 pages, no figures

On the theory and applications of modern cosmography [CL]

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http://arxiv.org/abs/1511.06532


Cosmography represents an important branch of cosmology which aims to describe the universe without the need of postulating \emph{a priori} any particular cosmological model. All quantities of interest are expanded as a Taylor series around here and now, providing in principle, a way of directly matching with cosmological data. In this way, cosmography can be regarded a model-independent technique, able to fix cosmic bounds, although several issues limit its use in various model reconstructions. The main purpose of this review is to focus on the key features of cosmography, emphasising both the strategy for obtaining the observable cosmographic series and pointing out any drawbacks which might plague the standard cosmographic treatment. In doing so, we relate cosmography to the most relevant cosmological quantities and to several dark energy models. We also investigate whether cosmography is able to provide information about the form of the cosmological expansion history, discussing how to reproduce the dark fluid from the cosmographic sound speed. Following this, we discuss limits on cosmographic priors and focus on how to experimentally treat cosmographic expansions. Finally, we present some of the latest developments of the cosmographic method, reviewing the use of rational approximations, based on cosmographic Pad\’e polynomials. Future prospects leading to more accurate cosmographic results, able to better reproduce the expansion history of the universe are also discussed in detail.

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P. Dunsby and O. Luongo
Mon, 23 Nov 15
10/40

Comments: N/A

Convection-driven kinematic dynamos at low Rossby and magnetic Prandtl numbers: single mode solutions [CL]

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http://arxiv.org/abs/1511.06164


The onset of dynamo action is investigated within the context of a newly developed low Rossby, low magnetic Prandtl number, convection-driven dynamo model. The model represents an asymptotically exact form of an $\alpha^2$ mean field dynamo model in which the small-scale convection is represented explicitly by the finite amplitude, single mode convective solutions first investigated by Bassom and Zhang (Geophys.~Astrophys.~Fluid Dyn., \textbf{76}, p.223, 1994). Both steady and oscillatory convection are considered for a variety of horizontal planforms. The kinematic helicity is observed to be a monotonically increasing function of the Rayleigh number; as a result, very small magnetic Prandtl number dynamos can be found for a sufficiently large Rayleigh number. All dynamos are found to be oscillatory with an oscillation frequency that increases as the strength of the convection is increased and the magnetic Prandtl number is reduced. Single mode solutions which exhibit boundary layer behavior in the kinematic helicity show a decrease in the efficiency of dynamo action due to the enhancement of magnetic diffusion in the boundary layer regions. For a given value of the Rayleigh number, lower magnetic Prandtl number dynamos are excited for the case of oscillatory convection in comparison to steady convection.

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M. Calkins, K. Julien, S. Tobias, et. al.
Fri, 20 Nov 15
42/55

Comments: 13 pages, 12 figures

Indirect (source-free) integration method. II. Self-force consistent radial fall [CL]

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http://arxiv.org/abs/1511.04277


We apply our method of indirect integration, described in Part I, at fourth order, to the radial fall affected by the self-force. The Mode-Sum regularisation is performed in the Regge-Wheeler gauge using the equivalence with the harmonic gauge for this orbit. We consider also the motion subjected to a self-consistent and iterative correction determined by the self-force through osculating stretches of geodesics. The convergence of the results confirms the validity of the integration method. This work complements and justifies the analysis and the results appeared in Int. J. Geom. Meth. Mod. Phys., 11, 1450090 (2014).

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P. Ritter, S. Aoudia, A. Spallicci, et. al.
Mon, 16 Nov 15
33/57

Comments: To appear in Int. J. Geom. Meth. Mod. Phys

Indirect (source-free) integration method. I. Wave-forms from geodesic generic orbits of EMRIs [CL]

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http://arxiv.org/abs/1511.04252


The Regge-Wheeler-Zerilli (RWZ) wave-equation describes Schwarzschild-Droste black hole perturbations. The source term contains a Dirac distribution and its derivative. We have previously designed a method of integration in time domain. It consists of a finite difference scheme where analytic expressions, dealing with the wave-function discontinuity through the jump conditions, replace the direct integration of the source and the potential. Herein, we successfully apply the same method to the geodesic generic orbits of EMRI (Extreme Mass Ratio Inspiral) sources, at second order. An EMRI is a Compact Star (CS) captured by a Super Massive Black Hole (SMBH). These are considered the best probes for testing gravitation in strong regime. The gravitational wave-forms, the radiated energy and angular momentum at infinity are computed and extensively compared with other methods, for different orbits (circular, elliptic, parabolic, including zoom-whirl).

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P. Ritter, S. Aoudia, A. Spallicci, et. al.
Mon, 16 Nov 15
50/57

Comments: To appear in Int. J. Geom. Meth. Mod Phys

A complete and explicit solution to the three-dimensional problem of two fixed centres [EPA]

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http://arxiv.org/abs/1510.07959


We present for the first time an explicit, complete and closed-form solution to the three-dimensional problem of two fixed centres, based on Weierstrass elliptic and related functions. With respect to previous treatments of the problem, our solution is exact, valid for all initial conditions and physical parameters of the system (including unbounded orbits and repulsive forces), and expressed via a unique set of formulae. Various properties of the three-dimensional problem of two fixed centres are investigated and analysed, with a particular emphasis on quasi-periodic and periodic orbits, regions of motion and equilibrium points.

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F. Biscani and D. Izzo
Wed, 28 Oct 15
37/79

Comments: Accepted for publication in MNRAS. 15 pages, 12 figures

Scale-invariant gauge theories of gravity: theoretical foundations [CL]

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http://arxiv.org/abs/1510.06699


We consider the construction of gauge theories of gravity, focussing in particular on the extension of local Poincar\’e invariance to include invariance under local changes of scale. We work exclusively in terms of finite transformations, which allow for a more transparent interpretation of such theories in terms of gauge fields in Minkowski spacetime. Our approach therefore differs from the usual geometrical description of locally scale-invariant Poincar\’e gauge theory (PGT) and Weyl gauge theory (WGT) in terms of Riemann–Cartan and Weyl–Cartan spacetimes, respectively. In particular, we reconsider the interpretation of the Einstein gauge and also the equations of motion of matter fields and test particles in these theories. Inspired by the observation that the PGT and WGT matter actions for the Dirac field and electromagnetic field have more general invariance properties than those imposed by construction, we go on to present a novel alternative to WGT by considering an `extended’ form for the transformation law of the rotational gauge field under local dilations, which includes its `normal’ transformation law in WGT as a special case. The resulting `extended’ Weyl gauge theory (eWGT) has a number of interesting features that we describe in detail. In particular, we present a new scale-invariant gauge theory of gravity that accommodates ordinary matter and is defined by the most general parity-invariant eWGT Lagrangian that is at most quadratic in the eWGT field strengths, and we derive its field equations. We also consider the construction of PGTs that are invariant under local dilations assuming either the `normal’ or `extended’ transformation law for the rotational gauge field, but show that they are special cases of WGT and eWGT, respectively.

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A. Lasenby and M. Hobson
Fri, 23 Oct 15
36/63

Comments: 55 pages, 0 figures, submitted to Journal of Mathematical Physics

Multiscale functions, Scale dynamics and Applications to partial differential equations [CL]

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http://arxiv.org/abs/1509.01048


Modeling phenomena from experimental data, always begin with a \emph{choice of hypothesis} on the observed dynamics such as \emph{determinism}, \emph{randomness}, \emph{derivability} etc. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following : \emph{“With a finite set of data concerning a phenomenon, can we recover its underlying nature ?} From this problem, we introduce in this paper the definition of \emph{multi-scale functions}, \emph{scale calculus} and \emph{scale dynamics} based on the \emph{time-scale calculus} (see \cite{bohn}). These definitions will be illustrated on the \emph{multi-scale Okamoto’s functions}. The introduced formalism explains why there exists different continuous models associated to an equation with different \emph{scale regimes} whereas the equation is \emph{scale invariant}. A typical example of such an equation, is the \emph{Euler-Lagrange equation} and particularly the \emph{Newton’s equation} which will be discussed. Notably, we obtain a \emph{non-linear diffusion equation} via the \emph{scale Newton’s equation} and also the \emph{non-linear Schr\”odinger equation} via the \emph{scale Newton’s equation}. Under special assumptions, we recover the classical \emph{diffusion} equation and the \emph{Schr\”odinger equation}.

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J. Cresson and F. Pierret
Fri, 4 Sep 15
34/58

Comments: N/A

Friedmann–Lemaitre Cosmologies via Roulettes and Other Analytic Methods [CL]

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http://arxiv.org/abs/1508.06750


In this work a series of methods are developed for understanding the Friedmann equation when it is beyond the reach of the Chebyshev theorem. First it will be demonstrated that every solution of the Friedmann equation admits a representation as a roulette such that information on the latter may be used to obtain that for the former. Next the Friedmann equation is integrated for a quadratic equation of state and for the Randall–Sundrum II universe, leading to a harvest of a rich collection of new interesting phenomena. Finally an analytic method is used to isolate the asymptotic behavior of the solutions of the Friedmann equation, when the equation of state is of an extended form which renders the integration impossible, and to establish a universal exponential growth law.

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S. Chen, G. Gibbons and Y. Yang
Fri, 28 Aug 15
3/49

Comments: 40 pages, no figures

Stochastic Eternal Inflation in a Bianchi Type I Universe [CL]

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http://arxiv.org/abs/1508.02670


In this paper, we analyze a Bianchi Type I model with a scalar field in a chaotic inflation potential, $V(\phi) = \frac{1}{2}\phi^2$ in the context of stochastic eternal inflation. We use the typical slow-roll approximation in combination with expansion-normalized variables in an orthonormal frame approach to obtain a dynamical system which describes the dynamics of the shear anisotropy and the inflaton field. We first show that the dynamics of the inflaton field can be decoupled from the dynamics of the shear anisotropy. We then use a fixed-points analysis in combination with global techniques from topological dynamical systems theory to prove that the cosmological model under consideration isotropizes irrespective of an inflationary epoch, which has also described by other authors who have investigated a Bianchi Type I model under similar configurations. We then show that for inflation to occur, the amount of anisotropy must be very small.
We also give a description of the stochastic dynamics of the inflaton field by using techniques from stochastic calculus. We show that the Klein-Gordon equation becomes a stochastic differential equation with a highly nonlinear drift term. In this case, the deceleration parameter itself becomes a random variable, and we give details regarding when such a model can undergo inflation. We finally derive the form of the long-term, stationary probability distribution of the inflaton field, and show that it has the form of a double-well potential. We then calculate the probability of inflation occurring based on this approach. We conclude the paper by performing some numerical simulations of the stochastic differential equation describing the dynamics of the inflaton field. We conjecture that even in the case of stochastic eternal inflation, one requires precise initial conditions for inflation to occur.

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I. Kohli and M. Haslam
Wed, 12 Aug 15
50/50

Comments: N/A

The three-body problem [EPA]

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http://arxiv.org/abs/1508.02312


The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more than 300 years. In this paper, we present a review of the three-body problem in the context of both historical and modern developments. We describe the general and restricted (circular and elliptic) three-body problems, different analytical and numerical methods of finding solutions, methods for performing stability analysis, search for periodic orbits and resonances, and application of the results to some interesting astronomical and space dynamical settings. We also provide a brief presentation of the general and restricted relativistic three-body problems, and discuss their astronomical applications.

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Z. Musielak and B. Quarles
Tue, 11 Aug 15
14/57

Comments: 49 pages, 10 figures, Published in Reports on Progress in Physics

Cascading Multicriticality in Nonrelativistic Spontaneous Symmetry Breaking [CL]

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http://arxiv.org/abs/1507.06992


Without Lorentz invariance, spontaneous global symmetry breaking can lead to multicritical Nambu-Goldstone modes with a higher-order low-energy dispersion $\omega\sim k^n$ ($n=2,3,\ldots$), whose naturalness is protected by polynomial shift symmetries. Here we investigate the role of infrared divergences and the nonrelativistic generalization of the Coleman-Hohenberg-Mermin-Wagner (CHMW) theorem. We find novel cascading phenomena with large hierarchies between the scales at which the value of $n$ changes, leading to an evasion of the “no-go” consequences of the relativistic CHMW theorem.

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T. Griffin, K. Grosvenor, P. Horava, et. al.
Tue, 28 Jul 15
21/70

Comments: 5 pages, 1 figure