Dispersion Relations for Cold Plasma Around the Horizon of Schwarzschild–de Sitter Black Hole

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.