Shear viscosity, relaxation and collision times in spherically symmetric spacetimes

TL;DR

This paper investigates shear viscosity in spherically symmetric spacetimes, deriving evolution equations and analyzing relaxation times for dark matter WIMPS, highlighting differences between full and truncated models.

Contribution

It introduces a novel interpretation of anisotropic pressure as shear viscosity in LTB spacetimes and analyzes relaxation times using Extended Irreversible Thermodynamics.

Findings

Relaxation times are similar to collision times for the full model.

Truncated model fails to capture transient transition phenomena.

Numerical solutions provide insights into dark matter behavior post-decoupling.

Abstract

We interpret as shear viscosity the anisotropic pressure that emerges in inhomogeneous spherically symmetric spacetimes described by the Lemaitre-Tolman-Bondi (LTB) metric in a comoving frame. By assuming that local isotropic pressure and energy density satisfy a generic ideal gas equation of state, we reduce the field equations to a set of evolution equations based on auxiliary quasi-local variables. We examine the transport equation of shear viscosity from Extended Irreversible Thermodynamics and use a numerical solution of the evolution equations to obtain the relaxation times for the full and "truncated" versions. Considering a gas of cold dark matter WIMPS after its decoupling from the cosmic fluid, we show that the relaxation times for the general equation are qualitatively analogous to collision times, while the truncated version is inadequate to describe transient phenomena of transition to equilibrium.