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.
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References
Petterson J.A. (1974). Phys. Rev. D 10: 3166
Israel W. (1967). Phys. Rev. 164: 1776
Israel W. (1968). Commun. Math. Phys. 8: 245
Hawking S. (1972). Commun. Math. Phys. 25: 152
Robinson D. (1974). Phys. Rev. D 10: 458
Arnowitt R., Deser S. and Misner C.W. (1962). Gravitation: An Introduction to Current Research.. Wiley, New York
Tarfulea, N.: Ph.D. Thesis, University of Minnesota (2004)
Thorne K.S. and Macdonald D.A. (1982). Mon. Not. R. Astron. Soc. 198: 339
Thorne K.S. and Macdonald D.A. (1982). Mon. Not. R. Astron. Soc. 198: 345
Thorne K.S., Price R.H. and Macdonald D.A. (1986). Black Holes: The Membrane Paradigm. Yale University Press, New Haven
Holcomb K.A. and Tajima T. (1989). Phys. Rev. D 40: 3809
Holcomb K.A. (1990). Astrophys. J. 362: 381
Dettmann C.P., Frankel N.E. and Kowalenko V. (1993). Phys. Rev. D 48: 5655
Khanna R. (1998). Mon. Not. R. Astron. Soc. 294: 673
Antón, L., Zanotti, O., Miralles, J.A., Martí, J.A., M A Ibáñez, J., Font, J.A., Pons, J.A.: Astrophys. J. 637, 296 (2006)
Anile A.M. (1989). Relativistic Fluids and Magneto-Fluids with Applications in Astrophysics and Plasma Physics. Cambridge University Press, London
Komissarov S.S. (2002). Mon. Not. R. Astron. Soc. 336: 759
Komissarov S.S. (2004). Mon. Not. R. Astron. Soc. 350: 407
Zhang X.-H. (1989). Phys. Rev. D 39: 2933
Zhang X.-H. (1989). Phys. Rev. D 40: 3858
Tsikarishvili E.G., Rogava A.D., Lominadze J.G. and Javakhishvili J.I. (1992). Phys. Rev. A 46: 1078
Mofiz U.A. (2005). BRAC Univ. J. II 83: 83
Regge T. and Wheeler J.A. (1957). Phys. Rev. 108: 1063
Zerilli F. (1970). Phys. Rev. D 2: 2141
Zerilli F. (1970). J. Math. Phys. 11: 2203
Zerilli F. (1970). Phys. Rev. Lett. 24: 737
Price, R.H.: Phys. Rev. D 5, 2419 (1972); ibid 2439
Hanni R.S. and Ruffini R. (1973). Phys. Rev. D 8: 3259
Wald R.M. (1974). Phys. Rev. D 10: 1680
Sakai J. and Kawata T. (1980). J. Phys. Soc. Jpn. 49: 747
Buzzi, V., Hines, K.C., Treumann, R.A.: Phys. Rev. D 51, 6663 (1995); ibid 6677
Das A.C. (2004). Space Plasma Physics: An Introduction. Narosa Publishing House, New Delhi
Jackson J.D. (1999). Classical Electrodynamics. Wiley, New York
Achenbach J.D. (1973). Wave Propogation in Elastic Solids. North-Holland, Oxford
Veselago V.G. (1968). Sov. Phys. Usp. 10: 509
Mackay T.G., Lakhtakia A. and Setiawan S. (2005). New J. Phys. 7: 171
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Sharif, M., Sheikh, U. Cold plasma dispersion relations in the vicinity of a Schwarzschild black hole horizon. Gen Relativ Gravit 39, 1437–1465 (2007). https://doi.org/10.1007/s10714-007-0465-8
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DOI: https://doi.org/10.1007/s10714-007-0465-8