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On a Relation Between the Bach Equation and the Equation of Geometrodynamics

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Abstract

The Bach equation and the equation of geometrodynamics are based on two quite different physical motivations, but in both approaches, the conformal properties of gravitation play the key role. In this paper we present an analysis of the relation between these two equations and show that the solutions of the equation of geometrodynamics are of a more general nature. We show the following non-trivial result: there exists a conformally invariant Lagrangian, whose field equation generalizes the Bach equation and has as solutions those Ricci tensors which are solutions to the equation of break geometrodynamics.

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Authors and Affiliations

  1. Russian Federal Nuclear Center - All-Russian S&R Institute of Experimental Physics. Sarov, Nizhnii Novgorod Region, 607190, Russia

    M. V. Gorbatenko & A. V. Pushkin

  2. Institut für Mathematik, Universität Potsdam, Am Neuen Palais 10, D-14469, Potsdam, Germany

    H.-J. Schmidt

Authors
  1. M. V. Gorbatenko
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  2. A. V. Pushkin
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  3. H.-J. Schmidt
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Correspondence to H.-J. Schmidt.

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Gorbatenko, M.V., Pushkin, A.V. & Schmidt, HJ. On a Relation Between the Bach Equation and the Equation of Geometrodynamics. General Relativity and Gravitation 34, 9–22 (2002). https://doi.org/10.1023/A:1015258219933

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  • DOI: https://doi.org/10.1023/A:1015258219933

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