An Action Principle for Relativistic MHD

TL;DR

This paper introduces a covariant action principle for ideal relativistic MHD using Eulerian variables, extending the Poisson bracket framework to incorporate magnetic field divergence-free conditions and Lie-dragged forms.

Contribution

It develops a new covariant action principle for relativistic MHD, incorporating a divergence-free magnetic field variable and Lie-dragged forms, advancing the theoretical framework.

Findings

Introduces a divergence-free 4-vector for magnetic field

Provides a covariant action principle for relativistic MHD

Discusses implications and extensions of the formalism

Abstract

A covariant action principle for ideal relativistic magnetohydrodynamics (MHD) in terms of natural Eulerian field variables is given. This is done by generalizing the covariant Poisson bracket theory of Marsden et al., which uses a noncanonical bracket to effect constrained variations of an action functional. Various implications and extensions of this action principle are also discussed. Two significant by-products of this formalism are the introduction of a new divergence-free 4-vector variable for the magnetic field, and a new Lie-dragged form for the theory.