The near equilibrium Einstein-Boltzmann system with a simplified collision term

TL;DR

This paper develops a simplified relativistic kinetic theory using a BGK-type collision term, deriving a self-consistent Einstein-Boltzmann system for homogeneous models with viscosity and heat flow.

Contribution

It introduces a simplified collision model and formulates a self-consistent Einstein-Boltzmann system for specific spacetime models.

Findings

Derived first-order differential equations for homogeneous models.

Established a relativistic kinetic framework with simplified collision term.

Connected kinetic theory with Einstein's equations in a new way.

Abstract

A simplified relativistic kinetic theory for gases with internal degrees of freedom, based on a BGK-type collision term, is considered. First the Boltzmann equation is rewritten in tetrad form and then thermal coefficients are determined to first order in the Chapman-Enskog expansion for general spacetimes. The results are used to construct a self-consistent system of first order differential equations, equivalent to the Einstein-Boltzmann system, for some spatially homogeneous models with viscosity and heat flow.