Shear viscosity, relaxation and collision times in spherically symmetric spacetimes

Details Shear viscosity, relaxation and collision times in spherically symmetric spacetimes Shear viscosity, relaxation and collision times in spherically symmetric spacetimes

2008-12-23

arxiv.org/abs/0812.4430v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Invited contribution in "Casimir effect and Cosmology", special volume on the occasion of 70th birthday of Prof. I. Brevik, co

Scientific paper

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.

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