# Relativistic magnetohydrodynamics

## TL;DR

This paper develops the theoretical framework for relativistic magnetohydrodynamics, including electromagnetic effects, transport coefficients, and wave modes, providing a comprehensive description of plasma behavior in relativistic regimes.

## Contribution

It introduces the equations of relativistic MHD with polarization and electric fields, enumerates transport coefficients, and derives constraints and formulas for their calculation.

## Key findings

- Identified transport coefficients and their constraints due to entropy production.
- Derived dispersion relations for plasma waves in different states.
- Connected conventional and dual formulations of magnetohydrodynamics.

## Abstract

We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion. We enumerate the transport coefficients at leading order in derivatives, including electrical conductivities, viscosities, and thermodynamic coefficients. We find the constraints on transport coefficients due to the positivity of entropy production, and derive the corresponding Kubo formulas. For the neutral state in a magnetic field, small fluctuations include Alfven waves, magnetosonic waves, and the dissipative modes. For the state with a non-zero dynamical charge density in a magnetic field, plasma oscillations gap out all propagating modes, except for Alfven-like waves with a quadratic dispersion relation. We relate the transport coefficients in the "conventional" magnetohydrodynamics (formulated using Maxwell's equations in matter) to those in the "dual" version of magnetohydrodynamics (formulated using the conserved magnetic flux).