Discriminating the Weyl type in higher dimensions using scalar curvature invariants

Details Discriminating the Weyl type in higher dimensions using scalar curvature invariants Discriminating the Weyl type in higher dimensions using scalar curvature invariants

Aug 2011

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011gregr..43.2199c&link_type=abstract

General Relativity and Gravitation, Volume 43, Issue 8, pp.2199-2207

Physics

Higher Dimensions, Lorentz Manifolds, Algebraic Classification, Polynomial Scalar Curvature Invariants, Black Hole Spacetimes

Scientific paper

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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