Acausality-driven instabilities in transient relativistic viscous hydrodynamics

TL;DR

This paper analyzes the origins of instabilities in relativistic viscous hydrodynamics models caused by superluminal information propagation, distinguishing between stable, unstable, and ill-posed regimes through analytical and numerical methods.

Contribution

It introduces a new analytical solution to identify different regimes of acausality and instability in relativistic viscous fluid models, validated by numerical simulations.

Findings

Stable regimes can be either causal or acausal.

Numerical instabilities align with analytically predicted unstable regimes.

The analytical solution helps distinguish between different instability regimes.

Abstract

We investigate non-linear instabilities stemming from superluminal propagation of information in Israel-Stewart-like models of relativistic viscous fluid dynamics. In relativity, the characteristic speed of propagation of information, $w$, and the speed of the fluid, $v$, allow us to differentiate between regimes of the hydrodynamic equations that are acausal but stable ($w>1$), unstable ($v^{2} w^{2} \geq 1$), and covariantly ill-posed ($w^{2} \leq 0$). As an analytical benchmark, we present a new solution that illustrates these distinct regimes. We compare this analytical solution to the result of a numerical relativistic viscous fluid dynamics solver, and confirm that the analytical result can be recovered numerically in the stable regime, whether causal or acausal. The onset of numerical instabilities is further found to occur in the regime predicted by the analytical solution.