Dispersion relations for a cold plasma around a Schwarzschild Anti-de Sitter black hole

We investigate the wave properties of the cold plasma near the event horizon of a Schwarzschild Anti-de Sitter (SAdS) black hole. The Fourier analyzed perturbed 3+1 general relativistic magnetohydrodynamics (GRMHD) equations are taken on the basis of which the complex dispersion relations are obtained for non-rotating, rotating non-magnetized and rotating magnetized backgrounds. The wave number and the phase and the group velocities and the refractive index are obtained (exposed graphically) to study the dispersive properties of the medium near the event horizon.