Dispersion Modes of Hot Plasma for Schwarzschild de-Sitter Horizon in a Veselago Medium

We analyze the dispersion modes of hot plasma around Schwarzschild de-Sitter event horizon in the presence of Veselago medium. For this purpose, we apply ADM 3+1 formalism to develop GRMHD equations for the Schwarzschild de-Sitter spacetime. Implementation of linear perturbation yields perturbed GRMHD equations that are used for the Fourier analysis of rotating (non-magnetized and magnetized) plasma. Wave analysis is described by the graphical representation of the wave vector, refractive index, change in refractive index, phase and group velocities. The outcome of this work supports the validity of Veselago medium.