Covariant gyrokinetic description of relativistic plasmas

A fundamental aspect of many plasma-related astrophysical problems is the kinetic description of magnetized relativistic plasmas in intense gravitational fields, such as in accretion disks around compact gravitating bodies. The goal of this paper is to formulate a gyrokinetic description for a Vlasov-Maxwell plasma within the framework of general relativity. A closed set of relativistic gyrokinetic equations, consisting of the collisionless gyrokinetic equation and corresponding expressions for the four-current density, is derived for an arbitrary four-dimensional coordinate system. General relativity effects are taken into account via the tetrad formalism. The guiding-center dynamics of charged particles and the gyrokinetic transformation are obtained accurate to the second order of the ratio of the Larmor radius to the nonuniformity scale length. The wave terms with arbitrary wavelength $(k\rho_{\mathrm L}\sim1)$ are described in the second-order (nonlinear) approximation with respect to the amplitude of the wave. The same approximations are used in the derivation of the gyrophase-averaged Maxwell equations. The derivation is based on the perturbative Lagrangian approach with a fully relativistic, four-dimensional covariant formulation. Its results improve on existing limitations of the gyrokinetic theory