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Annales Henri Poincaré

, Volume 16, Issue 7, pp 1509–1550 | Cite as

A Spacetime Characterization of the Kerr-NUT-(A)de Sitter and Related Metrics

  • Marc Mars
  • José M. M. SenovillaEmail author
Article

Abstract

A characterization of the Kerr-NUT-(A)de Sitter metric among four dimensional Λ-vacuum spacetimes admitting a Killing vector ξ is obtained in terms of the proportionality of the self-dual Weyl tensor and a natural self-dual double two-form constructed from the Killing vector. This result recovers and extends a previous characterization of the Kerr and Kerr-NUT metrics (Mars, Class Quant Grav 16:2507–2523, 1999). The method of proof is based on (i) the presence of a second Killing vector field which is built in terms of geometric information arising from the Killing vector ξ exclusively, and (ii) the existence of an interesting underlying geometric structure involving a Riemannian submersion of a conformally related metric, both of which may be of independent interest. Other related metrics can also be similarly characterized, in particular the Λ < 0 “black branes” recently used in AdS/CFT correspondence to describe, via holography, the physics of Quark–Gluon plasma.

Keywords

Black Hole Cosmological Constant Killing Vector Weyl Tensor Riemann Tensor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Instituto de Física Fundamental y MatemáticasUniversidad de SalamancaSalamancaSpain
  2. 2.Física TeóricaUniversidad del País VascoBilbaoSpain

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