Shear Viscosity in the Post-quasistatic Approximation

TL;DR

This paper investigates the evolution of anisotropic, dissipative matter distributions in General Relativity using the post-quasi-static approximation, focusing on shear viscosity effects during collapse or expansion.

Contribution

It introduces an application of the post-quasi-static approximation to model shear viscosity and dissipation in self-gravitating spheres, with new models based on Schwarzschild and Tolman VI solutions.

Findings

Viscosity-induced anisotropy controls collapse or expansion.

Matching interior solutions with Vaidya exterior is achieved.

Models demonstrate the impact of shear viscosity on evolution.

Abstract

We apply the post-quasi--static approximation, an iterative method for the evolution of self-gravitating spheres of matter, to study the evolution of anisotropic non-adiabatic radiating and dissipative distributions in General Relativity. Dissipation is described by viscosity and free-streaming radiation, assuming an equation of state to model anisotropy induced by the shear viscosity. We match the interior solution, in non-comoving coordinates, with the Vaidya exterior solution. Two simple models are presented, based on the Schwarzschild and Tolman VI solutions, in the non--adiabatic and adiabatic limit. In both cases the eventual collapse or expansion of the distribution is mainly controlled by the anisotropy induced by the viscosity.