Dispersion Relations for Isothermal Plasma around the Horizon of Reissner-Nordström-de Sitter Black Hole

We formulate the general relativistic magnetohydrodynamic equations for isothermal plasma in spatially flat Reissner-Nordström-de Sitter metric by using 3+1 split of spacetime. Respective perturbed equations are linearized for rotating magnetized surroundings. These are then Fourier analyzed and the corresponding dispersion relations are obtained. These relations are discussed both analytically and numerically in order to investigate the nature of waves with positive angular frequency around the horizon.