Toward General Relativistic Magnetohydrodynamics Simulations in Stationary Nonvacuum Spacetimes

Abstract Accretion of magnetized gas on compact astrophysical objects such as black holes (BHs) has been successfully modeled using general relativistic magnetohydrodynamic (GRMHD) simulations. These simulations have largely been performed in the Kerr metric, which describes the spacetime of a vacuum and stationary spinning BH in general relativity (GR). The simulations have revealed important clues to the physics of accretion flows and jets near the BH event horizon and have been used to interpret recent Event Horizon Telescope images of the supermassive BHs M87* and Sgr A*. The GRMHD simulations require the spacetime metric to be given in horizon-penetrating coordinates such that all metric coefficients are regular at the event horizon. Only a few metrics, notably the Kerr metric and its electrically charged spinning analog, the Kerr–Newman metric, are currently available in such coordinates. We report here horizon-penetrating forms of a large class of stationary, axisymmetric, spinning metrics. These can be used to carry out GRMHD simulations of accretion on spinning, nonvacuum BHs and non-BHs within GR, as well as accretion on spinning objects described by non-GR metric theories of gravity.