Heat flux in the presence of a gravitational field in a simple dilute fluid: an approach based in general relativistic kinetic theory to first order in the gradients

TL;DR

This paper uses relativistic kinetic theory to show how a gravitational field influences heat flux in a dilute fluid, highlighting effects that vanish in the non-relativistic limit.

Contribution

It introduces a novel approach by removing molecular acceleration from Boltzmann's equation, demonstrating gravity-driven heat flux in a relativistic fluid.

Findings

Gravity induces a heat flux in relativistic dilute fluids.

The effect disappears in the non-relativistic limit.

The approach is based on geodesic particle motion in a Schwarzschild-like metric.

Abstract

Richard C. Tolman analyzed the relation between a temperature gradient and a gravitational field in an equilibrium situation. In 2012, Tolman\textquoteright s law was generalized to a non-equilibrium situation for a simple dilute relativistic fluid. The result in that scenario, obtained by introducing the gravitational force through the molecular acceleration, couples the heat flux with the metric coefficients and the gradients of the state variables. In the present paper it is shown, by \textquotedblleft suppressing\textquotedblright{} the molecular acceleration in Boltzmann\textquoteright s equation, that a gravitational field drives a heat flux. This procedure corresponds to the description of particle motion through geodesics, in which a Newtonian limit to the Schwarzschild metric is assumed. The effect vanishes in the non-relativistic regime, as evidenced by the direct evaluation of the corresponding limit.