Isothermal plasma wave properties of the Schwarzschild de-Sitter black hole in a Veselago medium

Abstract

In this paper, we study wave properties of isothermal plasma for the Schwarzschild de-Sitter black hole in a Veselago medium. We use ADM 3 + 1 formalism to formulate general relativistic magnetohydrodynamical (GRMHD) equations for the Schwarzschild de-Sitter spacetime in Rindler coordinates. Further, Fourier analysis of the linearly perturbed GRMHD equations for the rotating (non-magnetized and magnetized) background is taken whose determinant leads to a dispersion relation. We investigate wave properties by using graphical representation of the wave vector, the refractive index, change in refractive index, phase and group velocities. Also, the modes of wave dispersion are explored. The results indicate the existence of the Veselago medium.

Hot plasma modes across Reissner–Nördstrom–de Sitter horizon in a Veselago medium

“…It is followed by previous work [31] that inclusion of positive cosmological constant in non-rotating black hole may reveal more information about magnetosphere. Here we have inspected that addition of charge and cosmological constant is beneficial to attain normal dispersion at majority of points in the region, however, most of the waves move towards event horizon.…”

“…GRMHD equations are governed from basic MHD equations in account with Maxwells electrodynamical equations. 3 + 1 GRMHD equations for RN-dS metric in a Veselago medium become [31].…”

“…In non-magnetized environment, B = 0 = ξ leads to a 5 = 0 = a 6 , in the Fourier analyzed GRMHD equations (2.11)-(2.14) [31]. In order to solve Fourier analyzed equations numerically, we assume µ = 1+α 2 2 and ρ = p =…”

“…Sharif and Mukhtar [30] discussed dispersion relations for Schwarzschild horizon in unusual medium. Sharif and Noureen [31] determined dispersion modes of isothermal and hot plasma across SdS horizon for negative index medium. Recently, wave behavior around Reissner-Nördstrom spacetime is worked out [33].…”

“…Application of linear perturbation in perfect GRMHD equations (A1)-(A5) and insertion of Eq. (2.6) leads to component form of linearly perturbed GRMHD equations [31], provided in the Appendix. Further, to take Fourier analysis of perturbed GRMHD equations, metric dependence is considered in the following way…”