  Low density plasmas are characterized by a large scale separation between the
gyromotion of particles around local magnetic fields and the macroscopic scales
of the system, often making global kinetic simulations computationally
intractable. The guiding center formalism has been proposed as a powerful tool
to bridge the gap between these scales. Despite its usefulness, the guiding
center approach has been formulated successfully only in flat spacetimes,
limiting its applicability in astrophysical settings. Here, we present a new
covariant formalism that leads to kinetic equations in the guiding center limit
that are valid in arbitrary spacetimes. Through a variety of experiments, we
demonstrate that our equations capture all known gyro-center drifts while
overcoming one severe limitation imposed on numerical algorithms by the fast
timescales of the particle gyromotion. This formalism will enable explorations
of a variety of global plasma kinetic phenomena in the curved spacetimes around
black holes and neutron stars.

High Energy Astrophysical Phenomena;General Relativity and Quantum Cosmology;Plasma Physics