Covariant magnetoionic theory -- I. Ray propagation

Accretion on to compact objects plays a central role in high-energy astrophysics. In these environments, both general relativistic and plasma effects may have a significant impact upon the propagation of photons. We present a fully general relativistic magnetoionic theory, capable of tracing rays in the geometrical optics approximation through a magnetized plasma in the vicinity of a compact object. We consider both the cold and warm, ion and pair plasmas. When plasma effects become large the two plasma eigenmodes follow different ray trajectories, resulting in a large observable polarization. This has implications for accreting systems ranging from pulsars and X-ray binaries to active galactic nuclei.