On the linear causality and stability of third-order relativistic dissipative fluid dynamics

TL;DR

This paper examines the linear causality and stability of third-order relativistic dissipative fluid dynamics, revealing issues with the existing formulation and proposing a modified, stable, and causal theory under linear conditions.

Contribution

It identifies the linear acausality and instability in the existing third-order fluid dynamics theory and introduces a modified version that ensures linear causality and stability.

Findings

Original theory is linearly acausal and unstable.

Tuning transport coefficients cannot fix instabilities.

Proposed modification achieves linear causality and stability.

Abstract

We analyze the linear causality and stability of third-order fluid dynamics considering perturbations around a global equilibrium state. We investigate the formulation derived from kinetic theory, using the Chapman-Enskog expansion, in PRC 88, 021903, which was shown to be in excellent agreement with solutions of the microscopic theory. From this analysis, we demonstrate that this theory is linearly acausal and unstable and that such instabilities cannot be corrected by tuning the transport coefficients. We then propose a modification of this theory, valid only in the linear regime, that can be constructed to be linearly causal and stable and obtain the conditions the transport coefficients must satisfy in order for this to be the case.