  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 scale separation 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 a number of 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.
