New developments in relativistic magnetohydrodynamics

TL;DR

This paper reviews recent theoretical advances in relativistic magnetohydrodynamics (RMHD), highlighting new formulations, computational methods, and the role of chirality in plasma instabilities, with future research directions.

Contribution

It introduces novel formulations of RMHD based on magnetic flux conservation, discusses advanced kinetic and quantum field theoretical approaches, and explores chirality effects in plasma dynamics.

Findings

Formulation of RMHD from magnetic flux conservation perspective.

Calculation of transport coefficients using kinetic theory and quantum field theory.

Analysis of collective modes and instabilities influenced by chirality.

Abstract

Relativistic magnetohydrodynamics (RMHD) provides an extremely useful description of the low-energy long-wavelength phenomena in a variety of physical systems from quark-gluon plasma in heavy-ion collisions to matters in supernovas, compact stars, and early universe. We review the recent theoretical progresses of RMHD, such as a formulation of RMHD from the perspective of magnetic flux conservation using the entropy-current analysis, the nonequilibrium statistical operator approach applied to quantum electrodynamics, and the relativistic kinetic theory. We discuss how the transport coefficients in RMHD are computed in kinetic theory and perturbative quantum field theories. We also explore the collective modes and instabilities in RMHD with a special emphasis on the role of chirality in a parity-odd plasma. We also give some future prospects of RMHD, including the interaction with spin hydrodynamics and the new kinetic framework with magnetic flux conservation.