Higher-Dimensional Black Holes: Hidden Symmetries and Separation of Variables
arXiv:0802.0322 · doi:10.1088/0264-9381/25/15/154005
Abstract
In this paper, we discuss hidden symmetries in rotating black hole spacetimes. We start with an extended introduction which mainly summarizes results on hidden symmetries in four dimensions and introduces Killing and Killing-Yano tensors, objects responsible for hidden symmetries. We also demonstrate how starting with a principal CKY tensor (that is a closed non-degenerate conformal Killing-Yano 2-form) in 4D flat spacetime one can "generate" 4D Kerr-NUT-(A)dS solution and its hidden symmetries. After this we consider higher-dimensional Kerr-NUT-(A)dS metrics and demonstrate that they possess a principal CKY tensor which allows one to generate the whole tower of Killing-Yano and Killing tensors. These symmetries imply complete integrability of geodesic equations and complete separation of variables for the Hamilton-Jacobi, Klein-Gordon, and Dirac equations in the general Kerr-NUT-(A)dS metrics.
33 pages, no figures, updated references and corrected typos
References in corpus (42)
- General Kerr-NUT-AdS Metrics in All Dimensions
- Gravitational Perturbations of Higher Dimensional Rotating Black Holes: Tensor Perturbations
- Complete Integrability of Geodesic Motion in General Kerr-NUT-AdS Spacetimes
- Classification of the Weyl Tensor in Higher Dimensions and Applications
- `Hidden' Symmetries of Higher Dimensional Rotating Black Holes
- Hidden Symmetry of Higher Dimensional Kerr-NUT-AdS Spacetimes
- Quasinormal modes of D-dimensional de Sitter spacetime
- Rotating Black Holes in Higher Dimensional Einstein-Maxwell Gravity
- Massive scalar field quasi-normal modes of higher dimensional black holes
- Robinson-Trautman spacetimes in higher dimensions
- Type D Einstein spacetimes in higher dimensions
- Closed conformal Killing-Yano tensor and Kerr-NUT-de Sitter spacetime uniqueness
- Electromagnetic Properties of Kerr-Anti-de Sitter Black Holes
- Separability of Dirac equation in higher dimensional Kerr-NUT-de Sitter spacetime
- Charged Rotating Black Holes in Odd Dimensions
- On conformal Killing-Yano tensors for Plebanski-Demianski family of solutions
- Quasi-Normal Modes of Brane-Localised Standard Model Fields II: Kerr Black Holes
- Separability of the Hamilton-Jacobi and Klein-Gordon Equations in Kerr-de Sitter Metrics
- Constants of Geodesic Motion in Higher-Dimensional Black-Hole Spacetimes
- Kerr-NUT-de Sitter Curvature in All Dimensions
- Rotating Einstein-Maxwell-Dilaton Black Holes in D Dimensions
- Dirac quasinormal modes of D-dimensional de Sitter spacetime
- Closed conformal Killing-Yano tensor and geodesic integrability
- Complete Set of Commuting Symmetry Operators for the Klein-Gordon Equation in Generalized Higher-Dimensional Kerr-NUT-(A)dS Spacetimes
- Electromagnetic quasinormal modes of D-dimensional black holes
- Particle Motion and Scalar Field Propagation in Myers-Perry Black Hole Spacetimes in All Dimensions
- Higher dimensional rotating black holes in Einstein-Maxwell theory with negative cosmological constant
- Robinson-Trautman spacetimes with an electromagnetic field in higher dimensions
- Stationary strings and branes in the higher-dimensional Kerr-NUT-(A)dS spacetimes
- Integrability and the Kerr-(A)dS black hole in five dimensions
- A Note on Separability of Field Equations in Myers-Perry Spacetimes
- Explicit Toric Metric on Resolved Calabi-Yau Cone
- Kerr-Schild Structure and Harmonic 2-forms on (A)dS-Kerr-NUT Metrics
- High-energy black hole production
- Electromagnetic Field in Higher-Dimensional Black-Hole Spacetimes
- On the parameters of the Kerr-NUT-(anti-)de Sitter space-time
- Resolutions of Cones over Einstein-Sasaki Spaces
- Rotating Black Holes in Higher Dimensions
- Charged-rotating black holes and black strings in higher dimensional Einstein-Maxwell theory with a positive cosmological constant
- A Killing tensor for higher dimensional Kerr-AdS black holes with NUT charge
- Separability in Cohomogeneity-2 Kerr-NUT-AdS Metrics
- Creating semiclassical black holes in collider experiments and keeping them on a string
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- Free motion around black holes with discs or rings: between integrability and chaos - II
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- Multicritical Phase Transitions in Multiply Rotating Black Holes
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- Geometry of Lax pairs: particle motion and Killing-Yano tensors
- Dynamics, symmetries, anomaly and vortices in a rotating cosmic string background
- On hidden symmetries of extremal Kerr-NUT-AdS-dS black holes
- Integrability Conditions for Killing-Yano Tensors and Conformal Killing-Yano Tensors
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- New currents with Killing-Yano tensors
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- Uniqueness of Rotating Charged Black Holes in Five-Dimensional Minimal Gauged Supergravity
- Uses of Killing and Killing-Yano Tensors
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- Hidden Symmetries and Black Holes
- The precession of particle spin in spherical symmetric spacetimes
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- Coupling constant metamorphosis, Fermat principle and light propagation in Kerr metric
- Brane Symmetries Revisited: Symmetries of Tensile and Tensionless Branes in Possibly Degenerate Metrics and their Manifestations
- Higher-dimensional black holes with multiple equal rotations