Analytic solution of the Boltzmann equation in an expanding system

TL;DR

This paper derives an exact analytical solution to the relativistic Boltzmann equation for a massless gas in an expanding universe, revealing its non-equilibrium dynamics and mapping it to a static non-relativistic system.

Contribution

It presents the first exact analytical solution of the Boltzmann equation in an expanding relativistic system, reformulating it as coupled moment equations.

Findings

Exact solution for a specific initial condition

Mapping of relativistic non-equilibrium behavior to non-relativistic Maxwell molecules

Insight into non-equilibrium dynamics of expanding relativistic gases

Abstract

For a massless gas with constant cross section in a homogeneous, isotropically expanding spacetime we reformulate the relativistic Boltzmann equation as a set of non-linear coupled moment equations. For a particular initial condition this set can be solved exactly, yielding the first analytical solution of the Boltzmann equation for an expanding system. The non-equilibrium behavior of this relativistic gas can be mapped onto that of a homogeneous, static non-relativistic gas of Maxwell molecules.