http://arxiv.org/abs/2003.04609
Bulk viscosity plays a key role in several astrophysical phenomena linked to neutron stars, from the damping of modes of oscillation in mature stars to the dynamics of the hot remnant of a binary merger. To quantitatively model these systems and constrain the imprint of the equation of state of dense matter it is, however, necessary to resort to a general relativistic description of bulk viscosity. Several prescriptions exist to modify the standard Navier-Stokes equations, which are parabolic and lead to non-causal solutions, to obtain hyperbolic equations that can be used in a relativistic setting. The connection between microphysics and the parameters introduced is not, however, always transparent. In this paper we present a relativistic formalism where any thermodynamic process which contributes to the bulk viscosity is modelled as a set of chemical reactions, whose reaction coordinates are abstract parameters describing the displacement from local thermodynamic equilibrium. The result is a non-equilibrium thermodynamic theory for bulk-viscous fluids which does not rely on any near-equilibrium assumption, and naturally gives rise to telegraph-type equations for the reaction processes. We present also two concrete applications of our theory, to the bulk viscosity in neutron stars and to a non interacting neutron gas and compare our formulation with that of Israel and Stewart (1979), which for a mature neutron star emerges as a perturbative expansion of our theory near equilibrium.
L. Gavassino, M. Antonelli and B. Haskell
Wed, 11 Mar 20
15/65
Comments: 30 pages, 5 figures, submitted to PRD