Effects of Schwarzschild Black Hole Horizon on Isothermal Plasma Wave Dispersion

TL;DR

This paper investigates how the horizon of a Schwarzschild black hole influences plasma wave dispersion using GRMHD equations, revealing conditions for normal and anomalous dispersion and the role of rotation in wave behavior.

Contribution

It formulates and analyzes the linearized 3+1 GRMHD equations in Schwarzschild spacetime, exploring wave dispersion in non-rotating and rotating black hole magnetospheres.

Findings

Identification of normal and anomalous dispersion regimes.

Discovery of Veselago medium properties in plasma near the horizon.

Rotation is necessary for negative phase velocity propagation.

Abstract

The 3+1 GRMHD equations for Schwarzschild spacetime in Rindler coordinates with isothermal state of plasma are formulated. We consider the cases of non-rotating and rotating backgrounds with non-magnetized and magnetized plasmas. For these cases, the perturbed form of these equations are linearized and Fourier analyzed by introducing plane wave type solutions. The determinant of these equations in each case leads to two dispersion relations which give value of the wave number $k$. Using the wave number, we obtain information like phase and group velocities etc. which help to discuss the nature of the waves and their characteristics. These provide interesting information about the black hole magnetosphere near the horizon. There are cases of normal and anomalous dispersion. We find a case of normal dispersion of waves when the plasma admits the properties of Veselago medium. Our results agree with those of Mackay et al. according to which rotation of a black hole is required for negative phase velocity propagation.