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 Amp\`ere'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 Amp\`ere'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.