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

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

2007-05-19

arxiv.org/abs/0705.3579v1

Gen.Rel.Grav.39:1437-1465,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

27 pages, 11 figures accepted for publication in Gen. Relat. & Gravit

Scientific paper

10.1007/s10714-007-0465-8

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.

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