Proves that separability of geodesic motion and parallel transport along geodesics implies separability of the linear-in-spin Hamilton-Jacobi equation for test particles.
General Kerr-NUT-AdS Metrics in All Dimensions
6 Pith papers cite this work. Polarity classification is still indexing.
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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 \mu_i that are subject to the constraint \sum_i \mu_i^2=1. We find a coordinate reparameterisation in which the \mu_i variables are replaced by [D/2]-1 unconstrained coordinates y_\alpha, and having the remarkable property that the Kerr-AdS metric becomes diagonal in the coordinate differentials dy_\alpha. The coordinates r and y_\alpha now 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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roles
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background 2representative citing papers
Pole-skipping data encodes enough information to reconstruct the full metric of 3D rotating black holes and the radial functions of 4D separable rotating black holes, with Einstein equations becoming algebraic constraints on that data.
Explicit planar AdS multi-NUT spacetimes are built via axionic scalars or quadratic gravity, plus planar Kaluza-Klein monopoles with varying magnetic charges.
Torsion-modified vector equations separate in the Chong-Cvetič-Lu-Pope black hole via a generalized principal Killing-Yano tensor.
Conserved charges built from a Kerr-Schild background show the first law requires the Killing vector and AdS background to be held fixed, explaining why the rotating-frame energy F fails while E works, and why the geometric volume appears in the β Smarr relation.
Near-EVH limits of AdS6 and AdS7 black holes produce conformally related lower-dimensional black hole solutions in EMMD gravity, opening a potential path to microscopic entropy counting for non-AdS black holes via higher-dimensional AdS/CFT.
citing papers explorer
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Separability of the motion of spinning test particles in curved space-time
Proves that separability of geodesic motion and parallel transport along geodesics implies separability of the linear-in-spin Hamilton-Jacobi equation for test particles.
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Probing bulk geometry via pole skipping: from static to rotating spacetimes
Pole-skipping data encodes enough information to reconstruct the full metric of 3D rotating black holes and the radial functions of 4D separable rotating black holes, with Einstein equations becoming algebraic constraints on that data.
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Planar AdS multi-NUT spacetimes and Kaluza-Klein multi-monopoles
Explicit planar AdS multi-NUT spacetimes are built via axionic scalars or quadratic gravity, plus planar Kaluza-Klein monopoles with varying magnetic charges.
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Principal Tensor Strikes Again: Separability of Vector Equations with Torsion
Torsion-modified vector equations separate in the Chong-Cvetič-Lu-Pope black hole via a generalized principal Killing-Yano tensor.
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The Role of the Volume in Black Hole Thermodynamics
Conserved charges built from a Kerr-Schild background show the first law requires the Killing vector and AdS background to be held fixed, explaining why the rotating-frame energy F fails while E works, and why the geometric volume appears in the β Smarr relation.
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Probing decoupled Throats of AdS$_{D}$ Black Holes in $D=6,7$
Near-EVH limits of AdS6 and AdS7 black holes produce conformally related lower-dimensional black hole solutions in EMMD gravity, opening a potential path to microscopic entropy counting for non-AdS black holes via higher-dimensional AdS/CFT.