Theory and applications of the relativistic Boltzmann equation

TL;DR

This paper analyzes relativistic kinetic systems, deriving transport laws for charged particles under electromagnetic fields and studying heat flux in gravitational fields, revealing new relativistic effects on transport coefficients.

Contribution

It provides new derivations of Fourier and Ohm laws in relativistic contexts and explores the impact of gravity on heat flux and thermal conductivity in relativistic gases.

Findings

Derived Fourier and Ohm laws for relativistic charged particle systems.

Identified three contributions to heat flux in gravitational fields.

Found that thermal conductivity decreases with gravitational influence.

Abstract

In this work two systems are analyzed within the framework of the relativistic Boltzmann equation. One of them refers to a description of binary mixtures of electrons and protons and of electrons and photons subjected to external electromagnetic fields in special relativity. In this case the Fourier and Ohm laws are derived and the corresponding transport coefficients are obtained. In the other a relativistic gas under the influence of the Schwarzschild metric is studied. It is shown that the heat flux in Fourier's law in the presence of gravitational fields has three contributions, the usual dependence on the temperature gradient, and two relativistic contributions, one of them associated with an acceleration and another to a gravitational potential gradient. Furthermore it is shown that the transport coefficient of thermal conductivity decreases in the presence of a gravitational field. The dependence of the temperature field in the presence of a gravitational potential is also discussed.