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Discriminating the Weyl type in higher dimensions using scalar curvature invariants

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Abstract

We consider higher dimensional Lorentzian spacetimes which are currently of interest in theoretical physics. It is possible to algebraically classify any tensor in a Lorentzian spacetime of arbitrary dimensions using alignment theory. In the case of the Weyl tensor, and using bivector theory, the associated Weyl curvature operator will have a restricted eigenvector structure for algebraic types II and D, which leads to necessary conditions on the discriminants of the associated characteristic equation which can be manifestly expressed in terms of polynomial scalar curvature invariants. The use of such necessary conditions in terms of scalar curvature invariants will be of great utility in the study and classification of black hole solutions in more than four dimensions.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 3J5, Canada

    Alan Coley

  2. Faculty of Science and Technology, University of Stavanger, 4036, Stavanger, Norway

    Sigbjørn Hervik

Authors
  1. Alan Coley
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  2. Sigbjørn Hervik
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Correspondence to Alan Coley.

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Coley, A., Hervik, S. Discriminating the Weyl type in higher dimensions using scalar curvature invariants. Gen Relativ Gravit 43, 2199–2207 (2011). https://doi.org/10.1007/s10714-011-1174-x

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  • DOI: https://doi.org/10.1007/s10714-011-1174-x

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