The Boltzmann equation in special and general relativity

TL;DR

This paper derives relativistic gas equations from the Boltzmann equation using Chapman-Enskog methodology, applying them to cosmological and gravitational scenarios in special and general relativity.

Contribution

It introduces a relativistic model for the Boltzmann equation and applies it to cosmological and gravitational contexts, extending kinetic theory in relativity.

Findings

Relativistic constitutive equations derived from Chapman-Enskog method.

Application to a homogeneous isotropic universe with irreversible processes.

Analysis of a gas in a spherically symmetric gravitational field.

Abstract

Relativistic field equations for a gas in special and general relativity are determined from the Boltzmann equation. The constitutive equations are obtained from the Chapman-Enskog methodology applied to a relativistic model equation proposed by Anderson and Witting. Two applications in general relativity are considered: one refers to a gas in a homogeneous and isotropic Universe where irreversible processes are present during its evolution; in the other it is analyzed a gas under the influence of a spherically symmetrical non-rotating and uncharged source of the gravitational field.