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On a Five-Dimensional Version of the Goldberg-Sachs Theorem

  • Marcello OrtaggioEmail author
  • Vojtěch Pravda
  • Alena Pravdová
  • Harvey S. Reall
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 157)

Abstract

The recently developed generalization of the Goldberg-Sachs theorem to five-dimensional Einstein spacetimes is summarized. This generalization involves two steps. First it has been proven that in arbitrary dimension an Eistein spacetime admitting a multiple WAND admits also a multiple geodetic WAND. Second, in five dimensions, the \(3 \times 3\) optical matrix of such geodetic multiple WAND can be cast to one of three canonical forms, each determined by two free parameters.

Notes

Acknowledgments

The authors acknowledge support from research plan RVO: 67985840 and research grant no P203/10/0749.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Marcello Ortaggio
    • 1
    Email author
  • Vojtěch Pravda
    • 1
  • Alena Pravdová
    • 1
  • Harvey S. Reall
    • 2
  1. 1.Institute of MathematicsAcademy of SciencesPrague 1Czech Republic
  2. 2.DAMTPCentre for Mathematical Sciences, University of CambridgeCambridgeUK

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