An analysis of wave properties of isothermal plasma around Reissner-Nordström black hole

The 3+1 spacetime split is used in a preliminary investigation of waves propagating in a medium of isothermal plasma in the vicinity of event horizon of Reissner-Nordström planar analogue. The general relativistic magnetohydrodynamic equations for isothermal have been investigated there. The dispersion relations are obtained by using linear perturbation and Fourier analyze techniques for non-rotating and rotating, non-magnetized and magnetized environment. The wave number, phase velocity, group velocity etc. are shown to discuss the nature of the waves.