“Space-time tells matter how to move; matter tells space-time how to curve”
John Archibald Wheeler
Abstract
We envisage a black hole perturbed by a force-free magnetic field (FFMF) outside and attempt to determine its structure. We suppose the metric that describes this black hole is of the static spherical type, that is Schwarzschild, and the energy–momentum tensor emanating from an FFMF source perturbs this background metric, in this regard one can imagine a magnetic accretion disk around the black hole. By solving the equations for such a configuration, we will show that in addition to modifying the diagonal elements of the background metric, we will also see the non-zeroing of the off-diagonal elements of the general metric, one of the immediate consequences of which will be a static to stationary transition.
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This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.]
References
Aschwanden, M.J.: Physics of the Solar Corona. An Introduction. Praxis Publishing Ltd., Springer-Verlag, Chichester, Berlin (2004)
Chandrasekhar, S., Kendall, P.C.: On force-free magnetic fields. Astrophys. J. 126, 457C (1957)
Priest, E.: Magnetohydrodynamics of the Sun. Cambridge University Press, Cambridge (2014)
Marsh, G.E.: Force-Free Magnetic Fields: Solutions, Topology and Applications. World Scientific Publishing Co., Pte. Ltd., Singapore (1996)
Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability, 1st edn. Courier Corporation 2013, New York (1961)
Akiyama, K. et al.: First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring Astrophys. J. Lett. 875, ( pp 17) (2019)
Blandford, R.D., Znajek, R.L.: Electromagnetic extraction of energy from Kerr black holes. Mon. Notices R. Astron. Soc. 179, 433 (1977)
MacDonald, D., Thorne, K.S.: Black-hole electrodynamics: an absolutespace/universal-time formulation. Mon. Notices R. Astron. Soc. 198, 345 (1982)
McKinney, J.C., Narayan, R.: Disc–jet coupling in black hole accretion systems—I. General relativistic magnetohydrodynamical models. Mon. Not. R. Astron. Soc. 375, 513 (2007)
Thorne, K.S., MacDonald, D.: Electrodynamics in curved spacetime: 3 + 1 formulation. Mon. Notices R. Astron. Soc. 198, 339 (1982)
Thorne, K.S., Price, R.H., MacDonald, D.: Black Holes: The Membrane Paradigm. Yale, New Haven (1986)
Semenov, V., Dyadechkin, S., Punsly, B.: Simulations of jets driven by black hole rotation. Science 305, 978 (2004)
Punsly, B.: Black Hole Gravitohydromagnetics. Springer, Berlin (2001)
Brennan, T.D., Gralla, S.E., Jacobson, T.: Exact solutions to force-free electrodynamics in black hole backgrounds. Class. Quantum Gravity 30, 195012 (2013)
Blinder, S. M.: [arXiv:gr-qc/0409025 [gr-qc]]
Weinberg, S.: Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, 1st edn. Wiley, New York (1972)
Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation, 21th printing, W. H. Company, New York (1998)
Padmanabhan, T.: Gravitation Foundations and Frontiers, 1st printing. Cambridge University Press, Cambridge (2010)
Ryder, L.: Introduction to General Relativity, 1st printing. Cambridge University Press, Cambridge (2009)
Jackson, J.D.: Classical Electrodynamics, 3rd edn. Wiley, Hoboken (1999)
Reissner, H.: Über die Eigengravitation des elektrischen Feldes nach der Einsteinschen Theorie. Annalen der Physik 50(9), 106 (1916) (in German)
Newman, E.T., et al.: Metric of a rotating, charged mass. J. Math. Phys. 6, 918–919 (1965)
Acknowledgements
H.S. is grateful to Y. Sobouti who basically taught him the physics of the FFMFs.
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HS: Conceptualization, Investigation, Methodology, Visualization, Writing—original draft, review & editing.
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Sheikhahmadi, H. Schwarzschild Black Hole Perturbed by a Force-Free Magnetic Field. Found Phys 52, 93 (2022). https://doi.org/10.1007/s10701-022-00612-7
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DOI: https://doi.org/10.1007/s10701-022-00612-7