A Hybrid Algorithm for Drift-Kinetic Particle Dynamics within General Relativistic Magnetohydrodynamics Simulations of Black Holes Accretion Flows

Astrophysical plasmas in relativistic spacetimes, such as black hole accretion flows, are often weakly collisional and require kinetic modeling to capture non-local transport and particle acceleration. However, the extreme scale separation between microscopic and macroscopic processes limits the feasibility of fully kinetic simulations. A covariant guiding center formalism has recently been derived to address this challenge in curved spacetimes. We present a new hybrid numerical algorithm based on this formalism, which evolves the trajectories of charged particles over macroscopic timescales in GRMHD backgrounds. To address numerical instabilities in the equations of motion, we develop a semi-implicit integrator that ensures stable evolution in strong-field environments. We apply our method to GRMHD simulations of black hole accretion flows, demonstrating its accuracy and efficiency across a range of physical conditions.