The General Kerr-de Sitter metrics in all dimensions

By G. W. Gibbons, Hong Lu, D. Page, C. Pope. 2004

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We give the general Kerr–de Sitter metric in arbitrary space–time dimension D≥4, with the maximal number [(D−1)/2] of independent rotation parameters. We obtain the metric in Kerr–Schild form, where it is written as the sum of a de Sitter metric plus the square of a null-geodesic vector, and in generalised Boyer–Lindquist coordinates. The Kerr–Schild form is simpler for verifying that the Einstein equations are satisfied, and we have explicitly checked our results for all dimensions D≤11. We discuss the global structure of the metrics, and obtain formulae for the surface gravities and areas of the event horizons. We also obtain the Euclidean-signature solutions, and we construct complete non-singular compact Einstein spaces on associated SD−2 bundles over S2, infinitely many for each odd D≥5.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/6d9e7e02c6dc50eebe17cdcbce5c005252a61de5

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Citations in the corpus

Thermodynamics of Rotating Black Holes and Black Rings: Phase Transitions and Thermodynamic Volume (2014, background): “General Kerr-AdS black hole spacetimes [102, 103] are d-dimensional metrics that solve the Einstein equations with cosmological constant”
Comments on string theory backgrounds with non-relativistic conformal symmetry (2008, background): “In order to obtain the metric for the case of the black hole in AdS7 we simply need to start from the general rotating black holes in seven dimension as written in [29] (see also [51]).”
Reentrant phase transitions in rotating anti–de Sitter black holes (2013, background): “The associated thermodynamic quantities read (in Planck units) [17]”
Kerr-AdS/CFT correspondence in diverse dimensions (2008, unknown): “The general Kerr-AdS metrics in arbitrary higher dimensions were obtained in [9, 10].”
Holographic thermalization, quasinormal modes and superradiance in Kerr-AdS (2013, background): “It was then further generalized to include negative cosmological constant for the case of five dimensions in [64], and then to arbitrary dimensions by [65, 66].”
Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions (2008, methodology): “Following [30], we begin by defining two integers n and ǫ via d = 2n + ǫ with ǫ = d mod 2.”
Black hole enthalpy and an entropy inequality for the thermodynamic volume (2010, background): “r to the horizon, of the form (1.12), again, remarkably, gives rise to the expression on the right-hand side of (1.13) (if one uses the standard radial coordinate that appears in the metrics given in [11, 12]).2 However, this volume, which we shall now call V′, is not the one that gives rise to the ”
Large rotating AdS black holes from fluid mechanics (2007, methodology): “3) of [15] (we specialise to odd dimensions by setting the parameter ǫ in that equation to zero).”
Black Holes in Higher Dimensions (2008, background): “, it depends on a single (radial) coordinate [111, 112].”
Numerical methods for finding stationary gravitational solutions (2015, background): “If one also imposes asymptotic flatness, there are of course spherical black holes, including the higher dimensional versions of Kerr [171–173] and Kerr-AdS [331], namely Myers-Perry black holes [332, 333] and their AdS counterparts [334, 335].”
Black rings in (Anti)-de Sitter space (2008, methodology): “C Phase space of rotating AdS black holes Here we discuss the phase space of the rotating AdS black hole solution of [13] with more than one angular momentum (the case of a single angular momentum is discussed in the main text).”
Rotating black holes in gauged supergravities: Thermodynamics, supersymmetric limits, topological solitons and time machines (2005, background): “The general uncharged AdS black hole solutions were found in four dimensions in [11], in five dimensions in [12], and in all dimensions D ≥ 6 in [13, 14].”
General Kerr–NUT–AdS metrics in all dimensions (2006, methodology): “By making a change of variables analogous to the one considered long ago by Jacobi in the theory of constrained dynamical systems, we were able to rewrite the Kerr–AdS solutions of [4, 5] in such a way that the metrics become diagonal in a set of unconstrained latitude coordinates yα .”