General Kerr–NUT–AdS metrics in all dimensions

By W. Chen, Hsueh-I Lu, C. Pope, G. P, C. Mitchell. 2006

247 citations recorded by the source corpus.

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 μi that are subject to the constraint ∑iμ2i = 1. We find a coordinate reparametrization in which the μi variables are replaced by [D/2] − 1 unconstrained coordinates yα, and having the remarkable property that the Kerr–AdS metric becomes diagonal in the coordinate differentials dyα. The coordinates r and yα now appear in a very symmetrical way in the metric, leading to an immediate generalization 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 ⩾ 4, 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 Euclideanization, new families of Einstein–Sasaki metrics.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2b41b8b579c044959d8b1346b0f9d0ccc6ff2ddd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Enthalpy and the mechanics of AdS black holes (2009, result): “More recently amongst many other results, the extension of the Myers–Perry higher dimensional rotating black hole solutions [6] was found in [7, 8], solutions including NUT charge were constructed in [9, 10] and approximate black ring solutions in AdS were been studied in [11].”
The classical double copy for Taub–NUT spacetime (2015, background): “[69], and subsequently shown to have a multiple Kerr-Schild form [70], involving n = ⌊D/2⌋ linearly independent, mutually orthogonal null vector fields k i (here ⌊X⌋ denotes the integer part of X): gμν = ḡμν + n”
Kerr-AdS/CFT correspondence in diverse dimensions (2008, unknown): “Although we shall not be including the NUT parameters in our calculations, the form of the metrics obtained in [18] will be the most convenient one for our purposes.”
Extremal Black Hole/CFT Correspondence in (Guaged) Supergravities (2008, unknown): “ively, using global AdS2 coordinates, as ds2 = A −(1 +r2)dτ2 + dr2 1 +r2 + nX−1 α=1 F αdy2 + n−X1+ǫ i,j=1 ˜gij e˜i ˜ej , ˜ei = dφi +kirdτ, ki = 1 2πTi , Ti = − T′0 H Ω′0 i . (2.18) Here we follow [32] and use a set of unconstrained latitudinal coordinates yα, rather than the direction cosines µ as”
The Kerr-Schild double copy in curved spacetime (2017, background): “d eld Aa double copies to the graviton ~h , dened with respect to the background metric g . 8Examples involving more than two terms are the higher dimensional Taub-NUT-like solutions of refs. [93,94]. 10 Curved A h a A a _ aa' aa' + _ + Minkowski Minkowski Zeroth Copy Double Copy g _ Figur”