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Black Holes, Hidden Symmetry and Complete Integrability: Brief Review

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General Relativity, Cosmology and Astrophysics

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 177))

Abstract

This chapter contains a brief review of the remarkable properties of higher dimensional rotating black holes with the spherical topology of the horizon. We demonstrate that these properties are connected with and generated by a special geometrical object, the Principal Conformal Killing-Yano tensor (PCKYT). The most general solution, describing such black holes, Kerr-NUT-ADS metric, admits this structure. Moreover a solution of the Einstein Equations with (or without) a cosmological constant which possesses PCKYT is the Kerr-NUT-ADS metric. This object (PCKYT) is responsible for such remarkable properties of higher dimensional rotating black holes as: (i) complete integrability of geodesic equations and (ii) complete separation of variables of the important field equations.

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Acknowledgments

The author thanks David Kubiznak for useful remarks. The author thanks the Natural Sciences and Engineering Research Council of Canada and the Killam Trust for the financial support. He also appreciate the financial support from CNRS and the hospitality of the University of Tours, where this chapter was written.

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Authors and Affiliations

  1. Theoretical Physics Institute, University of Alberta, Edmonton, AB, T6G 2E1, Canada

    Valeri P. Frolov

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  1. Valeri P. Frolov
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Correspondence to Valeri P. Frolov .

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Editors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University, Praha 8, Czech Republic

    Jiří Bičák

  2. Faculty of Mathematics and Physics, Charles University, Praha 8, Czech Republic

    Tomáš Ledvinka

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Frolov, V.P. (2014). Black Holes, Hidden Symmetry and Complete Integrability: Brief Review. In: Bičák, J., Ledvinka, T. (eds) General Relativity, Cosmology and Astrophysics. Fundamental Theories of Physics, vol 177. Springer, Cham. https://doi.org/10.1007/978-3-319-06349-2_13

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