A numerical scheme for resistive relativistic magnetohydrodynamics without Ampère's Law

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 Ampère's law becomes stiff in the high conductivity limit which poses challenges to the numerical evolution. In this work, 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 Ampère's Law, thereby avoiding the stiffness problem. We also explain the relation of this higher-form model to a traditional description of resistive magnetohydrodynamics and how causality is guaranteed by introducing second order corrections.