Cold Plasma Dispersion Relations in the Vicinity of a Schwarzschild Black Hole Horizon

TL;DR

This paper derives and analyzes the dispersion relations of cold plasma near a Schwarzschild black hole horizon using general relativistic magnetohydrodynamics, revealing insights into wave behavior and information extraction limitations.

Contribution

It presents the first derivation of relativistic dispersion relations for cold plasma near a Schwarzschild black hole horizon, including effects of rotation and magnetization.

Findings

No information can be extracted from the black hole.

Negative phase velocity propagates in rotating backgrounds.

Waves with positive angular frequency exist near the horizon.

Abstract

We apply the ADM 3+1 formalism to derive the general relativistic magnetohydrodynamic equations for cold plasma in spatially flat Schwarzschild metric. Respective perturbed equations are linearized for non-magnetized and magnetized plasmas both in non-rotating and rotating backgrounds. These are then Fourier analyzed and the corresponding dispersion relations are obtained. These relations are discussed for the existence of waves with positive angular frequency in the region near the horizon. Our results support the fact that no information can be extracted from the Schwarzschild black hole. It is concluded that negative phase velocity propagates in the rotating background whether the black hole is rotating or non-rotating.