Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-08-20
Gen.Rel.Grav.39:2095-2124,2007
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
23 pages, 8 figures accepted for publication in Gen. Relat. Grav
Scientific paper
10.1007/s10714-007-0505-4
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.
Sharif Mai
Sheikh Umber
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