Covariant Guiding Center Equations for Charged Particle Motions in General Relativistic Spacetimes

Low-density plasmas in curved spacetimes, such as those found in accretion flows around black holes, are challenging to model from first principles, owing to the large separation in scale between the characteristic scales of the microscopic processes and large mean free paths comparable to the system sizes. Kinetic approaches become necessary to capture the relevant physics but lack the dynamic range to model the global characteristics of the systems. In this paper, we develop new covariant guiding center equations of motion for charges in general relativistic spacetimes that are computationally tractable. We decompose the particle motion into a fast gyration, which we integrate analytically, and a slow drift of the guiding center, which can be solved numerically. We derive covariant conservation laws for the motions of the guiding centers and show, through several limiting cases, that the equations contain all known drift mechanisms. Finally, we present the general relativistic expressions for the various drift velocities in Schwarzschild spacetimes.