Relativistic magnetohydrodynamics

TL;DR

The paper develops a comprehensive relativistic magnetohydrodynamics framework with dynamical electromagnetic fields, incorporating polarization and derivative corrections. It systematically enumerates one-derivative transport coefficients, derives entropy-positivity and Kubo-formula constraints, and analyzes the spectrum of collective modes in neutral and charged magnetic states. It further connects the conventional Maxwell-in-matter MHD to a dual formulation based on conserved magnetic flux, demonstrating an equivalence of transport structures under suitable mappings. The work clarifies the roles of thermodynamic and non-equilibrium coefficients, provides explicit mode dispersions (Alfvén and magnetosonic) and gaps due to plasma oscillations, and offers a cohesive bridge between different MHD formalisms with concrete Kubo relations. These results lay the groundwork for applying relativistic MHD to strongly interacting systems and condensed-matter contexts where magnetic fields and polarization effects are essential.

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).