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Hamiltonian Formalism for Spinning Black Holes in General Relativity

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General Relativity, Cosmology and Astrophysics

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

Abstract

A Hamiltonian treatment of gravitationally interacting spinning black holes is presented based on a tetrad generalization of the Arnowitt-Deser-Misner (ADM) canonical formalism of general relativity. The formalism is valid through linear order in the single spins. For binary systems, higher-order post-Newtonian Hamiltonians are given in explicit analytic forms. A next-to-leading order in spin generalization is presented, others are mentioned. Comparisons between the Hamiltonian formalisms by ADM, Dirac, and Schwinger are made.

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Acknowledgments

The author thanks Stanley Deser for useful discussions.

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Authors and Affiliations

  1. Friedrich-Schiller-Universität Jena, Theoretisch-Physikalisches Institut, Max-Wien-Platz 1, 07743, Jena, Germany

    Gerhard Schäfer

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  1. Gerhard Schäfer
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Correspondence to Gerhard Schäfer .

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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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Schäfer, G. (2014). Hamiltonian Formalism for Spinning Black Holes in General Relativity. 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_7

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