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Differential invariants and exact solutions of the Einstein equations

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Abstract

In this paper (cf. Lychagin and Yumaguzhin, in Anal Math Phys, 2016) a class of totally geodesics solutions for the vacuum Einstein equations is introduced. It consists of Einstein metrics of signature (1,3) such that 2-dimensional distributions, defined by the Weyl tensor, are completely integrable and totally geodesic. The complete and explicit description of metrics from these class is given. It is shown that these metrics depend on two functions in one variable and one harmonic function.

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Authors and Affiliations

  1. University of Tromso, Tromsø, Norway

    Valentin Lychagin

  2. Institute of Control Sciences of RAS, Moscow, Russia

    Valentin Lychagin

  3. Program Systems Institute of RAS, Pereslavl-Zalessky, Russia

    Valeriy Yumaguzhin

Authors
  1. Valentin Lychagin
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  2. Valeriy Yumaguzhin
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Correspondence to Valeriy Yumaguzhin.

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Lychagin, V., Yumaguzhin, V. Differential invariants and exact solutions of the Einstein equations. Anal.Math.Phys. 7, 107–115 (2017). https://doi.org/10.1007/s13324-016-0130-z

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  • DOI: https://doi.org/10.1007/s13324-016-0130-z

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