Magnetohydrodynamics in stationary and axisymmetric spacetimes: a fully covariant approach

TL;DR

This paper develops a fully covariant, geometrical framework for general relativistic magnetohydrodynamics in stationary, axisymmetric spacetimes without assuming circularity, extending existing models and deriving new equilibrium equations.

Contribution

It introduces a fully covariant approach to GRMHD that generalizes previous models by not assuming circular spacetimes and derives new relativistic equilibrium equations.

Findings

First relativistic Soloviev transfield equation derived

Covariant Grad-Shafranov and Stokes equations obtained

Equilibrium equations for purely toroidal magnetic fields formulated

Abstract

A fully geometrical treatment of general relativistic magnetohydrodynamics (GRMHD) is developed under the hypotheses of perfect conductivity, stationarity and axisymmetry. The spacetime is not assumed to be circular, which allows for greater generality than the Kerr-type spacetimes usually considered in GRMHD. Expressing the electromagnetic field tensor solely in terms of three scalar fields related to the spacetime symmetries, we generalize previously obtained results in various directions. In particular, we present the first relativistic version of the Soloviev transfield equation, subcases of which lead to fully covariant versions of the Grad-Shafranov equation and of the Stokes equation in the hydrodynamical limit. We have also derived, as another subcase of the relativistic Soloviev equation, the equation governing magnetohydrodynamical equilibria with purely toroidal magnetic fields in stationary and axisymmetric spacetimes.