812 research outputs found
Separability and Killing Tensors in Kerr-Taub-NUT-de Sitter Metrics in Higher Dimensions
A generalisation of the four-dimensional Kerr-de Sitter metrics to include a
NUT charge is well known, and is included within a class of metrics obtained by
Plebanski. In this paper, we study a related class of Kerr-Taub-NUT-de Sitter
metrics in arbitrary dimensions D \ge 6, which contain three non-trivial
continuous parameters, namely the mass, the NUT charge, and a (single) angular
momentum. We demonstrate the separability of the Hamilton-Jacobi and wave
equations, we construct a closely-related rank-2 Staeckel-Killing tensor, and
we show how the metrics can be written in a double Kerr-Schild form. Our
results encompass the case of the Kerr-de Sitter metrics in arbitrary
dimension, with all but one rotation parameter vanishing. Finally, we consider
the real Euclidean-signature continuations of the metrics, and show how in a
limit they give rise to certain recently-obtained complete non-singular compact
Einstein manifolds.Comment: Author added, title changed, references added, focus of paper changed
to Killing tensors and separability. Latex, 13 page
Kerr-de Sitter Black Holes with NUT Charges
The four-dimensional Kerr-de Sitter and Kerr-AdS black hole metrics have
cohomogeneity 2, and they admit a generalisation in which an additional
parameter characterising a NUT charge is included. In this paper, we study the
higher-dimensional Kerr-AdS metrics, specialised to cohomogeneity 2 by
appropriate restrictions on their rotation parameters, and we show how they too
admit a generalisation in which an additional NUT-type parameter is introduced.
We discuss also the supersymmetric limits of the new metrics. If one performs a
Wick rotation to Euclidean spacetime signature, these yield new Einstein-Sasaki
metrics in odd dimensions, and Ricci-flat metrics in even dimensions. We also
study the five-dimensional Kerr-AdS black holes in detail. Although in this
particular case the NUT parameter is trivial, our investigation reveals the
remarkable feature that a five-dimensional Kerr-AdS ``over-rotating'' metric is
equivalent, after performing a coordinate transformation, to an under-rotating
Kerr-AdS metric.Comment: Latex, 21 page
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