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

作者：Mars Marc^*; Senovilla Jose M M

来源：Annales Henri Poincare, 2015, 16(7): 1509-1550.

DOI：10.1007/s00023-014-0343-3

A characterization of the Kerr-NUT-(A)de Sitter metric among four dimensional I >-vacuum spacetimes admitting a Killing vector xi 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 xi 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 I > < 0 "black branes" recently used in AdS/CFT correspondence to describe, via holography, the physics of Quark-Gluon plasma.

• 出版日期2015-7