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arXiv · hep-th/0604125

General Kerr-NUT-AdS Metrics in All Dimensions

W. Chen·H. Lu·C. N. Pope
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Abstract

The Kerr-AdS metric in dimension D has cohomogeneity [D/2]; the metric components depend on the radial coordinate r and [D/2] latitude variables μ_i that are subject to the constraint \sum_i μ_i^2=1. We find a coordinate reparameterisation in which the μ_i variables are replaced by [D/2]-1 unconstrained coordinates y_α, and having the remarkable property that the Kerr-AdS metric becomes diagonal in the coordinate differentials dy_α. The coordinates r and y_αnow appear in a very symmetrical way in the metric, leading to an immediate generalisation in which we can introduce [D/2]-1 NUT parameters. We find that (D-5)/2 are non-trivial in odd dimensions, whilst (D-2)/2 are non-trivial in even dimensions. This gives the most general Kerr-NUT-AdS metric in $D$ dimensions. We find that in all dimensions D\ge4 there exist discrete symmetries that involve inverting a rotation parameter through the AdS radius. These symmetries imply that Kerr-NUT-AdS metrics with over-rotating parameters are equivalent to under-rotating metrics. We also consider the BPS limit of the Kerr-NUT-AdS metrics, and thereby obtain, in odd dimensions and after Euclideanisation, new families of Einstein-Sasaki metrics.

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BibTeXRIS

W. Chen, H. Lu, C. N. Pope. 2006-05-23. General Kerr-NUT-AdS Metrics in All Dimensions. https://doi.org/10.1088/0264-9381%2F23%2F17%2F013

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