Stability and Causality in relativistic dissipative hydrodynamics

TL;DR

This paper examines the stability and causality issues in relativistic dissipative hydrodynamics, showing that acausality leads to instability and analyzing the stability of scaling solutions.

Contribution

It demonstrates the link between acausality and instability in relativistic hydrodynamics and discusses the stability of scaling solutions.

Findings

Acausality induces instability in the theory.

Scaling solutions can be unstable to perturbations.

The study clarifies the relationship between causality and stability.

Abstract

The stability and causality of the Landau-Lifshitz theory and the Israel-Stewart type causal dissipative hydrodynamics are discussed. We show that the problem of acausality and instability are correlated in relativistic dissipative hydrodynamics and instability is induced by acausality. We further discuss the stability of the scaling solution. The scaling solution of the causal dissipative hydrodynamics can be unstable against inhomogeneous perturbations.