Resistive relativistic magnetohydrodynamics without Amperes Law

TL;DR

This paper introduces a novel approach to resistive relativistic magnetohydrodynamics that avoids the stiffness issues of Amperes Law by employing higher form symmetry and a dual tensor formulation, enabling more stable simulations.

Contribution

It presents a new dual tensor formulation of resistive magnetohydrodynamics that bypasses Amperes Law, improving numerical stability in high conductivity regimes.

Findings

Enables stable numerical simulations without Amperes Law

Shows the relation between dual and traditional models

Ensures causality with second order corrections

Abstract

Resistive magnetohydrodynamics is thought to play a key role in transient astrophysical phenomena such as black hole flares and neutron star magnetospheres. When performing numerical simulations of resistive magnetohydrodynamics, one is faced with the issue that Amperes law becomes stiff in the high conductivity limit which poses challenges to the numerical evolution. We show that using a description of resistive magnetohydrodynamics based on higher form symmetry, one can perform simulations with a generalized dual Faraday tensor without having to use Amperes Law, thereby avoiding the stiffness problem. We also explain the relation of this dual model to a traditional description of resistive magnetohydrodynamics and how causality is guaranteed by introducing second order corrections.