Causality and stability of magnetohydrodynamics for an ultrarelativistic locally neutral two-component gas

TL;DR

This paper analyzes the causality and stability of a relativistic magnetohydrodynamics framework for a neutral two-component plasma, demonstrating its linear causality and stability, and comparing it with traditional models in astrophysics and heavy-ion collisions.

Contribution

It introduces a causally consistent and stable relativistic MHD formalism for massless particle plasmas, extending previous models and analyzing its applicability in high-energy physics.

Findings

The formalism is linearly causal and stable around equilibrium.

It differs qualitatively from the Israel-Stewart formalism in the linear regime.

Applicable to ultrarelativistic heavy-ion collisions.

Abstract

We investigate the causality and stability of the relativistic theory of magnetohydrodynamics derived in Phys. Rev. D 109, 096021 (2024) to describe a locally neutral two-component plasma of massless particles. We show that this formalism is linearly causal and stable around global equilibrium, for any value of the magnetic field and discuss its qualitative differences to the traditional Israel-Stewart formalism in the linear regime. Finally, we compare this framework with the magnetohydrodynamic model used in the study of astrophysical plasmas, in which only the longitudinal component of the shear-stress tensor is considered. We discuss the domain of applicability of this type of framework in the context of ultrarelativistic heavy-ion collisions.