Hot plasma waves in Schwarzschild magnetosphere

In this paper we examine the wave properties of a hot plasma living in a Schwarzschild magnetosphere. The 3+1 GRMHD perturbation equations are formulated for this scenario. These equations are Fourier analyzed and then solved numerically to obtain the dispersion relations for a non-rotating, rotating non-magnetized and rotating magnetized plasma. The wave vector is evaluated, which is used to calculate the refractive index. These quantities are shown in graphs which are helpful to discuss the dispersive properties of the medium near the event horizon.