Abstract
We prove that in Einstein-Maxwell theory the inequality (8π J )2+(4π Q 2)2 < A 2 holds for any sub-extremal axisymmetric and stationary black hole with arbitrary surrounding matter. Here J, Q, and A are angular momentum, electric charge, and horizon area of the black hole, respectively.
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References
Ansorg M., Pfister H.: A universal constraint between charge and rotation rate for degenerate black holes surrounded by matter. Class. Quantum Grav. 25, 035009 (2008)
Bardeen, J.M.: Rapidly rotating stars, disks, and black holes. In: Black holes (Les Houches), deWitt, C., deWitt, B.S., ed., London: Gordon and Breach, 1973, pp. 241–289
Booth I., Fairhurst S.: Extremality conditions for isolated and dynamical horizons. Phys. Rev. D 77, 084005 (2008)
Buttazzo G., Giaquinta M., Hildebrandt S.: One-dimensional variational problems. Clarendon Press, Oxford (1998)
Carter, B.: Black hole equilibrium states. In: Black Holes (Les Houches), deWitt, C., deWitt, B.S., ed., London: Gordon and Breach, 1973, pp. 57–214
Evans, L.C.: Partial Differential Equations. Providence, RI: Amer. Math. Soc. 2002
Hennig J., Ansorg M., Cederbaum C.: A universal inequality between the angular momentum and horizon area for axisymmetric and stationary black holes with surrounding matter. Class. Quantum Grav. 25, 162002 (2008)
Rauch J.: Partial Differential Equations. Springer, Berlin (1991)
Yosida K.: Functional Analysis. Springer, Berlin (1995)
Acknowledgement
We would like to thank Herbert Pfister for many valuable discussions and John Head for commenting on the manuscript. This work was supported by the Deutsche Forschungsgemeinschaft (DFG) through the Collaborative Research Centre SFB/TR7 “Gravitational wave astronomy” and by the International Max Planck Research School for “Geometric Analysis, Gravitation and String Theory”.
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Communicated by P.T. Chruściel
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Hennig, J., Cederbaum, C. & Ansorg, M. A Universal Inequality for Axisymmetric and Stationary Black Holes with Surrounding Matter in the Einstein-Maxwell Theory. Commun. Math. Phys. 293, 449–467 (2010). https://doi.org/10.1007/s00220-009-0889-y
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DOI: https://doi.org/10.1007/s00220-009-0889-y