A causality analysis of the linearized relativistic Navier-Stokes equations

TL;DR

This paper demonstrates that the linearized relativistic Navier-Stokes equations for an ideal gas at rest obey causality, challenging the necessity of Israel-Stewart formalism in relativistic fluid modeling.

Contribution

It provides a simple analysis showing causality in the linearized relativistic Navier-Stokes equations, questioning the need for more complex formalisms.

Findings

The linearized system obeys the causality principle.

Dispersion relation roots confirm causality.

Implications for relativistic heavy ion experiments.

Abstract

It is shown by means of a simple analysis that the linearized system of transport equations for a relativistic, single component ideal gas at rest obeys the \textit{antecedence principle}, which is often referred to as causality principle. This task is accomplished by examining the roots of the dispersion relation for such a system. This result is important for recent experiments performed in relativistic heavy ion colliders, since it suggests that the Israel-Stewart like formalisms may be unnecessary in order to describe relativistic fluids.