Exact non-equilibrium solutions of the Einstein-Boltzmann equations. II

TL;DR

This paper derives exact solutions to the Einstein-Boltzmann equations in cosmological models, revealing detailed thermodynamic and viscous properties, and illustrating implications for the Weyl Curvature Hypothesis.

Contribution

It provides the first exact non-equilibrium solutions of Einstein-Boltzmann equations in FRW and Bianchi I spacetimes, including explicit expressions for viscous pressures.

Findings

Bulk viscous pressure expression for FRW with relaxational collision term

Zero bulk viscosity in collision-free equilibrium with ongoing entropy production

Bianchi I solutions exhibit zero heat flux and bulk viscosity, but nonzero shear viscosity

Abstract

We find exact solutions of the Einstein-Boltzmann equations with relaxational collision term in FRW and Bianchi I spacetimes. The kinematic and thermodynamic properties of the solutions are investigated. We give an exact expression for the bulk viscous pressure of an FRW distribution that relaxes towards collision-dominated equilibrium. If the relaxation is toward collision-free equilibrium, the bulk viscosity vanishes - but there is still entropy production. The Bianchi I solutions have zero heat flux and bulk viscosity, but nonzero shear viscosity. The solutions are used to construct a realisation of the Weyl Curvature Hypothesis.