Electromagnetic waves in a strong Schwarzschild plasma

The physics of high-frequency electromagnetic waves in a general relativistic plasma with the Schwarzschild metric is studied. Based on the $3+1$ formalism, we conformalize Maxwell's equations. The derived dispersion relations for waves in the plasma contain the lapse function in the plasma parameters such as in the plasma frequency and cyclotron frequency, but otherwise look “flat.” Because of this property this formulation is ideal for nonlinear self-consistent particle [particle-in-cell (PIC)] simulation. Some of the physical consequences arising from the general relativistic lapse function as well as from the effects specific to the plasma background distribution (such as density and magnetic field) give rise to nonuniform wave equations and their associated phenomena, such as wave resonance, cutoff, and mode conversion. These phenomena are expected to characterize the spectroscopy of radiation emitted by the plasma around the black hole. PIC simulation results of electron-positron plasma are also presented.