Causality in dissipative relativistic magnetohydrodynamics

TL;DR

This paper investigates the causality properties of dissipative relativistic magnetohydrodynamics, demonstrating how linear analysis can sometimes determine non-linear causality, with a focus on a complex theory including resistive effects and multiple transport coefficients.

Contribution

It clarifies the relationship between linear and non-linear causality in dissipative relativistic fluids, especially in magnetohydrodynamics with resistive effects and multiple transport coefficients.

Findings

Linear causality analysis can determine non-linear causality in some cases.

The study applies to a complex magnetohydrodynamic theory with resistive and anisotropic effects.

Causality properties are understood from linearized analysis in the most general fluid frame.

Abstract

We explore the relationship between linear and non-linear causality in theories of dissipative relativistic fluid dynamics. While for some fluid-dynamical theories, a linearized causality analysis can be used to determine whether the full non-linear theory is causal, for others it can not. As an illustration, we study relativistic viscous magnetohydrodynamics supplemented by a neutral-particle current, with resistive corrections to the conservation of magnetic flux. The dissipative theory has 10 transport coefficients, including anisotropic viscosities, electric resistivities, and neutral-particle conductivities. We show how causality properties of this magnetohydrodynamic theory, in the most general fluid frame, may be understood from the linearized analysis.