Ideal MHD(-Einstein) Solutions Obeying The Force-Free Condition

TL;DR

This paper presents two new analytic solutions to ideal MHD equations in curved spacetimes, maintaining the force-free condition, and includes a self-consistent Einstein-iMHD solution with a Vaidya-(A)dS metric, along with verification code.

Contribution

It introduces two families of analytic solutions to ideal MHD in curved spacetimes that preserve the force-free condition and a self-consistent Einstein-iMHD solution with an explicit metric.

Findings

Solutions maintain the force-free condition in curved spacetime.

A self-consistent Einstein-iMHD solution with Vaidya-(A)dS metric.

Provision of Mathematica code for solution verification.

Abstract

We find two families of analytic solutions to the ideal magnetohydrodynamics (iMHD) equations, in a class of 4-dimensional (4D) curved spacetimes. The plasma current is null, and as a result, the stress-energy tensor of the plasma itself can be chosen to take a cosmological-constant-like form. Despite the presence of a plasma, the force-free condition - where the electromagnetic current is orthogonal to the Maxwell tensor - continues to be maintained. Moreover, a special case of one of these two families leads us to a fully self-consistent solution to the Einstein-iMHD equations: we obtain the Vaidya-(anti-)de Sitter metric sourced by the plasma and a null electromagnetic stress tensor. We also provide a Mathematica code that researchers may use to readily verify analytic solutions to these iMHD equations in any curved 4D geometry.