http://arxiv.org/abs/1904.07321
We propose a local Lagrangian for a point particle where its inertia part is modified in the regime of small accelerations and its potential energy is kept intact. This Lagrangian is such that for the standard gravitational central force it recovers the deep MOdified Newtonian Dynamics (MOND) (accelerations $\ll a_0\approx 10^{-10}$m\,s$^{-2}$) equations of motion in the case of a circular orbit. We test the stability of the equations in the gravitational scenario by slightly perturbing them. The perturbations turn on higher derivative terms which are unstable in the deep MOND regime and have timescales larger than 1-3 billion years. Thus, there always are regions in the outskirts of galaxies where instabilities are irrelevant. For intermediate MOND regimes, instability timescales should be smaller than 1 billion years. We interpret what this could mean astrophysically. We also present ways to probe our approach and describe some of its subtleties, especially related to the strong equivalence principle (violated in general) and how in some cases it could overcome Ostrogradsky’s instabilities (with naturally occurring piecewise Lagrangians). Our main conclusion is that our MOND-like proposal constitutes a possible recipe where Ostrogradsky instabilities could be `tamed’ (when their timescales are larger than the age of the universe and for some piecewise Lagrangians), besides being a falsifiable approach in various contexts. This is relevant to start addressing practical ways to separate MOND as modified gravity and as modified inertia.
R. Costa, G. Franzmann and J. Pereira
Wed, 17 Apr 19
25/75
Comments: 10 pages, no figures