General Relativistic Two-fluid Plasmas around a Schwarzschild Black Hole. WKB approximation I

Details General Relativistic Two-fluid Plasmas around a Schwarzschild Black Hole. WKB approximation I General Relativistic Two-fluid Plasmas around a Schwarzschild Black Hole. WKB approximation I

2010-08-28

arxiv.org/abs/1008.4838v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

21 pages, 8 figures

Scientific paper

The 3+1 formalism of Thorne, Price and Macdonald has been used to investigate the behavior of the Alfv\'en and high frequency transverse electromagnetic waves propagating in the two fluid plasmas around Schwarzschild black hole. The plasma is assumed to be in freefall in radial direction toward the event horizon. The main result of the present work seems to be the discovery of an instability caused by the general relativistic terms in the dispersion relation. We reformulate the relativistic two-fluid equations for wave perturbations. Using WKB approximation we derive the local dispersion relation for these waves and solve it numerically for the wave number k.

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