Cold plasma wave dispersion around the horizon of Reissner-Nordström-de Sitter black hole

We investigate the wave properties for cold plasma in the vicinity of the Reissner-Nordström-de Sitter black hole's horizon using 3+1 split of spacetime. The corresponding Fourier analyzed perturbed GRMHD equations are used to obtain the dispersion relations. These relations lead to the real values of the wave number k which are used to evaluate the quantities like phase and group velocities, etc. These have been discussed graphically in the neighborhood of the horizon. The outcomes obtained verify the conclusion of Mackay et al. according to which negative phase velocity exists for the case of rotating surroundings.