  Recent advances in black hole astrophysics, particularly the first visual
evidence of a supermassive black hole at the center of the galaxy M87 by the
Event Horizon Telescope (EHT), and the detection of an orbiting "hot spot"
nearby the event horizon of Sgr A* in the Galactic center by the Gravity
Collaboration, require the development of novel numerical methods to understand
the underlying plasma microphysics. Non-thermal emission related to such hot
spots is conjectured to originate from plasmoids that form due to magnetic
reconnection in thin current layers in the innermost accretion zone.
Resistivity plays a crucial role in current sheet formation, magnetic
reconnection, and plasmoid growth in black hole accretion disks and jets. We
included resistivity in the three-dimensional general-relativistic
magnetohydrodynamics (GRMHD) code BHAC and present the implementation of an
Implicit-Explicit scheme to treat the stiff resistive source terms of the GRMHD
equations. The algorithm is tested in combination with adaptive mesh refinement
to resolve the resistive scales and a constrained transport method to keep the
magnetic field solenoidal. Several novel methods for primitive variable
recovery, a key part in relativistic magnetohydrodynamics codes, are presented
and compared for accuracy, robustness, and efficiency. We propose a new
inversion strategy that allows for resistive-GRMHD simulations of low
gas-to-magnetic pressure ratio and highly magnetized regimes as applicable for
black hole accretion disks, jets, and neutron star magnetospheres. We apply the
new scheme to study the effect of resistivity on accreting black holes,
accounting for dissipative effects as reconnection.
