Resistive relativistic magnetohydrodynamics without Ampère’s law

Resistive magnetohydrodynamics is thought to play a key role in transient high-energy astrophysical phenomena such as flares from black hole 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.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 dual model to a traditional description of resistive magnetohydrodynamics and how causality is guaranteed by introducing second order corrections.