Solving the heat-flow problem with transient relativistic fluid dynamics

TL;DR

This paper develops a new relativistic fluid dynamics theory derived from kinetic theory that accurately models heat flow and dissipative phenomena, improving upon previous models like Israel-Stewart theory.

Contribution

The authors derive a comprehensive relativistic dissipative fluid theory from kinetic theory that captures heat flow phenomena, addressing limitations of prior models.

Findings

The new theory matches numerical solutions of the relativistic Boltzmann equation.

It accurately describes heat flow in relativistic fluids.

It improves the modeling of dissipative processes in relativistic fluid dynamics.

Abstract

Israel-Stewart theory is a causal, stable formulation of relativistic dissipative fluid dynamics. This theory has been shown to give a decent description of the dynamical behavior of a relativistic fluid in cases where shear stress becomes important. In principle, it should also be applicable to situations where heat flow becomes important. However, it has been shown that there are cases where Israel-Stewart theory cannot reproduce phenomena associated with heat flow. In this paper, we derive a relativistic dissipative fluid-dynamical theory from kinetic theory which provides a good description of all dissipative phenomena, including heat flow. We explicitly demonstrate this by comparing this theory with numerical solutions of the relativistic Boltzmann equation.