Post-Newtonian magnetohydrodynamics

TL;DR

This paper derives the post-Newtonian magnetohydrodynamics equations using a modern harmonic gauge approach, revealing magnetic field effects in spacetime curvature and providing relativistic corrections for self-gravitating plasma behavior.

Contribution

It introduces a novel derivation of post-Newtonian MHD equations using harmonic gauge, highlighting magnetic field effects in the metric and providing a complete set of equations for self-gravitating plasma.

Findings

Magnetic field appears in the time-time component of the metric.

Relativistic corrections to MHD equations are derived up to first post-Newtonian order.

A comprehensive set of equations for self-gravitating plasma in post-Newtonian gravity is provided.

Abstract

In this paper, we derive the post-Newtonian equations of the ideal Magnetohydrodynamics. To do so, we use the modern approach to post-Newtonian theory, where the harmonic gauge is used instead of the standard post-Newtonian gauge, and find the post-Newtonian metric in the presence of the electromagnetic fields. We show that although the electric field does not contribute in the metric and curvature of the spacetime, the magnetic field appears in the time-time component of the metric. The appearance of the magnetic field, in principle, leads to new relativistic contributions to the magnetohydrodynamic governing equations. Therefore, using the post-Newtonian metric, we find the relativistic corrections to the magnetohydrodynamic equations up to the first post-Newtonian order. In addition, as usage of this derivation, we obtain a complete set of equations by which the behavior of a self-gravitating plasma can be determined in post-Newtonian gravity.