  Accretion of magnetized gas on compact astrophysical objects such as black
holes 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 black hole (BH) in general relativity (GR). The simulations
have revealed important clues on the physics of accretion 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$^*$. GRMHD simulations
require the spacetime metric in horizon-penetrating coordinates such that all
metric coefficients are regular at the event horizon. The Kerr metric and its
electrically charged spinning analog, the Kerr-Newman metric, are currently the
only metrics 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.
