General-Relativistic Resistive Magnetohydrodynamics in three dimensions: formulation and tests

We present a new numerical implementation of the general-relativistic resistive magnetohydrodynamics (MHD) equations within the Whisky code. The numerical method adopted exploits the properties of Implicit-Explicit Runge-Kutta numerical schemes to treat the stiff terms that appear in the equations for small electrical conductivities. Using tests in one, two, and three dimensions, we show that our implementation is robust and recovers the ideal-MHD limit in regimes of very high conductivity. Moreover, the results illustrate that the code is capable of describing physical setups in all ranges of conductivities. In addition to tests in flat spacetime, we report simulations of magnetized nonrotating relativistic stars, both in the Cowling approximation and in dynamical spacetimes. Finally, because of its astrophysical relevance and because it provides a severe testbed for general-relativistic codes with dynamical electromagnetic fields, we study the collapse of a nonrotating star to a black hole. We show that also in this case our results are in very good agreement with the perturbative studies of the dynamics of electromagnetic fields in a Schwarzschild background and provide an accurate estimate of the electromagnetic efficiency of this process