Holonomy groups of Lorentzian manifolds: classification, examples, and applications

  • Anton Galaev

    Masaryk University, Brno, Czech Republic
  • Thomas Leistner

    The University of Adelaide, Australia
Holonomy groups of Lorentzian manifolds: classification, examples, and applications cover

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Abstract

We review recent developments in the theory of Lorentzian holonomy groups focussing on the classification results. We present the list of indecomposable, non-irreducible Lorentzian holonomy groups, explain the idea of its proof, and describe a method of constructing metrics which realise all the possible groups. This method is then used to construct many examples of metrics. Finally, we give some applications for the existence of parallel spinors and a short outlook on other signatures. As a new result we obtain the holonomy classification for indecomposable, non-irreducible Lorentzian Einstein spaces.