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Stationary Black-Hole Binaries: A Non-existence Proof

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General Relativity, Cosmology and Astrophysics

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

Abstract

We resume former discussions of the question, whether the spin-spin repulsion and the gravitational attraction of two aligned black holes can balance each other. Based on the solution of a boundary problem for disconnected (Killing) horizons and the resulting violation of characteristic black hole properties, we present a non-existence proof for the equilibrium configuration in question. From a mathematical point of view, this result is a further example for the efficiency of the inverse (“scattering”) method in non-linear theories.

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Notes

  1. 1.

    In the following, we also use the complex coordinates \(z=\rho +\mathrm {i}\zeta \) and \(\bar{z} = \rho -\mathrm {i}\zeta \). \(t\) is the time coordinate.

  2. 2.

    From this point of view, the Ernst potential of the Kerr solution depends on one real parameter and two dimensionless coordinates.

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Acknowledgments

We would like to thank Reinhard Meinel, Marcus Ansorg and Andreas Kleinwächter for many valuable discussions and Ben Whale for commenting on the manuscript.

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Authors and Affiliations

  1. Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07749, Jena, Germany

    Gernot Neugebauer

  2. Department of Mathematics and Statistics, University of Otago, P.O. Box 56, Dunedin, 9054, New Zealand

    Jörg Hennig

Authors
  1. Gernot Neugebauer
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  2. Jörg Hennig
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Correspondence to Jörg Hennig .

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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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Neugebauer, G., Hennig, J. (2014). Stationary Black-Hole Binaries: A Non-existence Proof. 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_9

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