Vortex-like solutions and internal structures of covariant ideal magnetohydrodynamics

TL;DR

This paper presents a covariant formulation of ideal relativistic magnetohydrodynamics, revealing vortex-like solutions and highlighting potential violations of standard assumptions due to large charge densities and discrepancies in flow and current relations.

Contribution

It introduces a covariant framework for ideal MHD, explores vortex solutions, and discusses implications for charge densities and the interpretation of flow and currents.

Findings

Existence of stationary vortex-like solutions in covariant ideal MHD.

Inhomogeneous Maxwell equations can produce large electric charge densities.

Flow four-vector and conserved currents are generally unrelated in this framework.

Abstract

We discuss a manifestly covariant formulation of ideal relativistic magnetohydrodynamics, which has been recently used in astrophysical and heavy-ion contexts, and compare it to other similar frameworks. We show that the covariant equations allow for stationary vortex-like solutions that represent generalizations of the perfect-fluid solutions describing systems in global equilibrium with rotation. Such solutions are further used to demonstrate that inhomogeneous Maxwell equations, implicitly included in the covariant framework, may generate very large electric charge densities. This suggests that solutions of the covariant formulation may violate in some cases the assumptions of standard ideal magnetohydrodynamics. Furthermore, we show that the flow four-vector and conserved currents obtained in the covariant approach are usually not related to each other, which hinders kinetic-theory interpretation of the obtained results.