The heat flux from a relativistic kinetic equation with a simplified collision kernel

TL;DR

This paper derives a relativistic heat flux expression using a simplified kinetic equation, showing it aligns with classical thermodynamics and providing explicit transport coefficients compared to previous studies.

Contribution

It introduces a relativistic kinetic model with a BGK-like collision operator that yields a heat flux consistent with classical thermodynamics, including explicit transport coefficients.

Findings

Heat flux is linearly related to temperature and density gradients.

Derived transport coefficients match or improve upon previous results.

Heat flux is not dependent on acceleration as in some theories.

Abstract

We show how using a special relativistic kinetic equation with a BGK- like collision operator the ensuing expression for the heat flux can be casted in the form required by Classical Irreversible Thermodynamics. Indeed, it is linearly related to the temperature and number density gradients and not to the acceleration as the so-called "first order in the gradients theories" contend. Here we calculate explicitly the ensuing transport coefficients and compare them with the results obtained by other authors.