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


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.


Black Hole Cosmological Constant Killing Vector Weyl Tensor Riemann Tensor 
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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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