Dispersion Relations for Cold Plasmas around Reissner-Nordstr\"om Black Holes

TL;DR

This paper derives dispersion relations for cold plasma near Reissner-Nordström black holes using GRMHD equations, revealing wave propagation characteristics including negative velocities in rotating magnetized environments.

Contribution

It introduces a linearized GRMHD framework for cold plasma around charged black holes and analyzes wave behavior in various magnetic and rotational conditions.

Findings

Negative phase and group velocities in rotating magnetized plasma

Wave propagation near black hole horizons

Dispersion relations derived for different plasma conditions

Abstract

We investigate the general relativistic magnetohydrodynamic (GRMHD) equations for cold plasma around the Reissner-Nordstr\"om 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.