Maxwell-Cattaneo's equation and the stability of fluctuations in the relativistic fluid

TL;DR

This paper demonstrates that introducing a Maxwell-Cattaneo law in relativistic fluid models eliminates generic instabilities, highlighting the importance of relaxation times and challenging the unphysical behavior of first order theories like Eckart's.

Contribution

It shows how Maxwell-Cattaneo's law stabilizes relativistic fluid fluctuations, providing evidence against the causality and instability issues in first order theories.

Findings

Maxwell-Cattaneo law removes instabilities in relativistic fluids.

Stabilization depends on the difference in relaxation times.

Eckart's equations are responsible for unphysical behavior.

Abstract

Extended theories are widely used in the literature to describe the relativistic fluid. The motivation for this is mostly due to the causality issues allegedly present in the first order theories. However, the decay of fluctuations in the system is also at stake when first order theories \emph{that couple heat with acceleration} are used. In this paper it is shown how the generic instabilities in relativistic fluids are not present when a Maxwell-Cattaneo type law is introduced in the system of hydrodynamic equations. Emphasis is made on the fact that the stabilization is only due to the difference in characteristic times for heat flux relaxation and instabilities onset. This gives further evidence that Eckart's like constitutive equations are responsible for the first order sytem exhibiting unphysical behavior.