We investigate the general relativistic magnetohydrodynamic (GRMHD) equations for cold plasma around the Reissner-Nordström black hole. Applying 3+1 spacetime split we linearize the perturbed equations for non-magnetized/magnetized plasma in both rotating and non-rotating background. By Fourier analyze we then derive dispersion relations and investigate the existence of waves with positive angular frequency in the vicinity of the black hole horizon. The analysis finds propagation of negative phase and group velocities for rotating magnetized surroundings.

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 ReissnerNordström 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 nonrotating and rotating, non-magnetized and magnetized environment. The wave number, phase velocity, group velocity etc. are shown to discuss the nature of the waves.

No abstract

In this paper, we investigate the wave properties of cold plasma in the vicinity of Schawarzchild–de Sitter black hole horizon using 3 + 1 formalism. The general relativistic magnetohydrodynamical equations are formulated for this space–time with the use of Rindler coordinates. We consider both the rotating and nonrotating surroundings with magnetized and nonmagnetized plasmas. Linear perturbation and Fourier analysis techniques are applied by introducing simple harmonic waves. We derive complex dispersion relation from the determinant of Fourier analyzed equations for each case which provides real and complex values of the wave number. From the wave number we determine the phase and group velocities, the refractive index etc., which are used to discuss the characteristics of the waves around the event horizon.