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.
arXiv comment33 pages, no figures, updated references and corrected typos
References in corpus (85)
- Black Holes at the LHC
- High Energy Colliders as Black Hole Factories: The End of Short Distance Physics
- Quasinormal behavior of the D-dimensional Schwarzshild black hole and higher order WKB approach
- Rotation and the AdS/CFT correspondence
- The General Kerr-de Sitter Metrics in All Dimensions
- Classical Black Hole Production in High-Energy Collisions
- Black Holes in Theories with Large Extra Dimensions: a Review
- A master equation for gravitational perturbations of maximally symmetric black holes in higher dimensions
- Black Holes Radiate Mainly on the Brane
- Rotating Black Holes in Higher Dimensions with a Cosmological Constant
- Eigenvalues and eigenfunctions of spin-weighted spheroidal harmonics in four and higher dimensions
- New Einstein-Sasaki Spaces in Five and Higher Dimensions
- Classification of the Weyl Tensor in Higher Dimensions
- SUSY in the sky
- General Kerr-NUT-AdS Metrics in All Dimensions
- Black hole formation in the grazing collision of high-energy particles
- Gravitational Radiation in D-dimensional Spacetimes
- Particle and light motion in a space-time of a five-dimensional rotating black hole
- Quantum Radiation from a 5-Dimensional Rotating Black Hole
- Gravitational Perturbations of Higher Dimensional Rotating Black Holes: Tensor Perturbations
- Quasinormal modes of Schwarzschild black holes in four and higher dimensions
- Complete Integrability of Geodesic Motion in General Kerr-NUT-AdS Spacetimes
- Black hole particle emission in higher-dimensional spacetimes
- Separability of Hamilton-Jacobi and Klein-Gordon Equations in General Kerr-NUT-AdS Spacetimes
- Classification of the Weyl Tensor in Higher Dimensions and Applications
- `Hidden' Symmetries of Higher Dimensional Rotating Black Holes
- Alignment and algebraically special tensors in Lorentzian geometry
- Killing-Yano Tensors, Rank-2 Killing Tensors, and Conserved Quantities in Higher Dimensions
- 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
- Stability of multidimensional black holes: complete numerical analysis
- Hawking Radiation from a (4+n)-Dimensional Rotating Black Hole on the Brane
- Dirac symmetry operators from conformal Killing-Yano tensors
- Type D Einstein spacetimes in higher dimensions
- Five Dimensional Rotating Black Hole in a Uniform Magnetic Field. The Gyromagnetic Ratio
- Separability and Killing Tensors in Kerr-Taub-NUT-de Sitter Metrics in Higher Dimensions
- Closed conformal Killing-Yano tensor and Kerr-NUT-de Sitter spacetime uniqueness
- Electromagnetic Properties of Kerr-Anti-de Sitter Black Holes
- Quantum Mechanics of Yano tensors: Dirac equation in curved spacetime
- 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
- Five-Dimensional Charged Rotating Black Holes
- 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
- Axisymmetric metrics in arbitrary dimensions
- Constants of Geodesic Motion in Higher-Dimensional Black-Hole Spacetimes
- Kerr-NUT-de Sitter Curvature in All Dimensions
- Kerr-de Sitter Black Holes with NUT Charges
- Conserved gravitational charges from Yano tensors
- Rotating Einstein-Maxwell-Dilaton Black Holes in D Dimensions
- The scalar perturbation of the higher-dimensional rotating black holes
- Electromagnetic quasinormal modes of D-dimensional black holes
- Closed conformal Killing-Yano tensor and geodesic integrability
- Dirac quasinormal modes of D-dimensional de Sitter spacetime
- Complete Set of Commuting Symmetry Operators for the Klein-Gordon Equation in Generalized Higher-Dimensional Kerr-NUT-(A)dS Spacetimes
- Particle Motion and Scalar Field Propagation in Myers-Perry Black Hole Spacetimes in All Dimensions
- The most general axially symmetric electrovac spacetime adimitting separable equations of motion
- Higher dimensional rotating black holes in Einstein-Maxwell theory with negative cosmological constant
- Conformal Yano-Killing tensor for the Kerr metric and conserved quantities
- Debye Potentials for Maxwell and Dirac Fields from a Generalisation of the Killing-Yano Equation
- Robinson-Trautman spacetimes with an electromagnetic field in higher dimensions
- A Note on Separability of Field Equations in Myers-Perry Spacetimes
- Integrability and the Kerr-(A)dS black hole in five dimensions
- Stationary strings and branes in the higher-dimensional Kerr-NUT-(A)dS spacetimes
- Explicit Toric Metric on Resolved Calabi-Yau Cone
- Integrability of Particle Motion and Scalar Field Propagation in Kerr-(Anti) de Sitter Black Hole Spacetimes in All Dimensions
- Sasaki-Einstein Twist of Kerr-AdS Black Holes
- 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
- A Rainich-like approach to the Killing-Yano tensors
- Asymptotic Conformal Yano--Killing Tensors for Schwarzschild Metric
- 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
- Stationary strings near a higher-dimensional rotating black hole
- Separability in Cohomogeneity-2 Kerr-NUT-AdS Metrics
- Creating semiclassical black holes in collider experiments and keeping them on a string
- A Note on Particles and Scalar Fields in Higher Dimensional Nutty Spacetimes
Cited by in corpus (90)
- Quasinormal modes of black holes: from astrophysics to string theory
- Black hole chemistry: thermodynamics with Lambda
- Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
- Black holes, hidden symmetries, and complete integrability
- The Kerr Metric
- A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds
- On the Vanishing of Love Numbers for Kerr Black Holes
- Super-Entropic Black Holes
- Analytic solutions of the geodesic equation in higher dimensional static spherically symmetric space-times
- Hidden Symmetries of Higher Dimensional Black Holes and Uniqueness of the Kerr-NUT-(A)dS spacetime
- Energetics and optical properties of -dimensional rotating black hole in pure Gauss-Bonnet gravity
- Hidden Symmetries of Dynamics in Classical and Quantum Physics
- Ultraspinning instability of rotating black holes
- Maxwell's Equations in the Myers-Perry Geometry
- Ultraspinning limits and super-entropic black holes
- Free motion around black holes with discs or rings: between integrability and chaos - II
- Separation of Maxwell equations in Kerr-NUT-(A)dS spacetimes
- Generalized hidden symmetries and the Kerr-Sen black hole
- Generalized Killing-Yano equations in D=5 gauged supergravity
- Dirac Equation in Kerr-NUT-(A)dS Spacetimes: Intrinsic Characterization of Separability in All Dimensions
- Commuting symmetry operators of the Dirac equation, Killing-Yano and Schouten-Nijenhuis brackets
- Killing(-Yano) Tensors in String Theory
- Symmetries of the Dirac operator with skew-symmetric torsion
- Scalar Love numbers and Love symmetries of 5-dimensional Myers-Perry black holes
- Analytic treatment of geodesics in five-dimensional Myers-Perry space--times
- Killing-Yano tensors and multi-hermitian structures
- Symmetries of supergravity black holes
- N=2 superparticle near horizon of extreme Kerr-Newman-AdS-dS black hole
- Black holes and the LHC: A review
- Dynamics of test particles in the general five-dimensional Myers-Perry spacetime
- Separability of Black Holes in String Theory
- Motion of the charged test particles in Kerr-Newman-Taub-NUT spacetime and analytical solutions
- Separability of Gravitational Perturbation in Generalized Kerr-NUT-de Sitter Spacetime
- Quasinormal modes of Proca fields in a Schwarzschild-AdS spacetime
- Separability of the massive Dirac's equation in 5-dimensional Myers-Perry black hole geometry and its relation to a rank-three Killing-Yano tensor
- Separability of massive field equations for spin-0 and spin-1/2 charged particles in the general non-extremal rotating charged black holes in minimal five-dimensional gauged supergravity
- Parallel-propagated frame along null geodesics in higher-dimensional black hole spacetimes
- Multicritical Phase Transitions in Multiply Rotating Black Holes
- Geodesic motion around a distorted static black hole
- Hidden symmetries of Eisenhart-Duval lift metrics and the Dirac equation with flux
- First-order symmetries of Dirac equation in curved background: a unified dynamical symmetry condition
- On the supersymmetric limit of Kerr-NUT-AdS metrics
- Separability of a modified Dirac equation in a five-dimensional rotating, charged black hole in string theory
- Near-Horizon Polarization as a Diagnostic of Black Hole Spacetime
- Local metrics admitting a principal Killing-Yano tensor with torsion
- Quasi-normal modes for doubly rotating black holes
- Symmetry operators and separability of massive Klein-Gordon and Dirac equations in the general 5-dimensional Kerr-(anti-)de Sitter black hole background
- A simple test for spacetime symmetry
- Geometry of Lax pairs: particle motion and Killing-Yano tensors
- Stationary Strings in the Spacetime of Rotating Black Holes in Five-Dimensional Minimal Gauged Supergravity
- Dynamics, symmetries, anomaly and vortices in a rotating cosmic string background
- Excitations of the Myers-Perry Black Holes
- Integrability Conditions for Killing-Yano Tensors and Conformal Killing-Yano Tensors
- On hidden symmetries of extremal Kerr-NUT-AdS-dS black holes
- Special Killing forms on toric Sasaki-Einstein manifolds
- Killing-Yano Tensors of Order n-1
- New currents with Killing-Yano tensors
- Rational first integrals of geodesic equations and generalised hidden symmetries
- General Wahlquist Metrics in All Dimensions
- Killing-Yano forms and Killing tensors on a warped space
- Dirac equation in Kerr-Taub NUT spacetime
- Scalar fields on λ-deformed cosets
- SUSY in the Spacetime of Higher-Dimensional Rotating Black Holes
- Killing-Yano tensor and supersymmetry of the self-dual Plebanski-Demianski solution
- Uniqueness of Rotating Charged Black Holes in Five-Dimensional Minimal Gauged Supergravity
- A Deformation of Sasakian Structure in the Presence of Torsion and Supergravity Solutions
- On symmetry operators for the Maxwell equation on the Kerr-NUT-(A)dS spacetime
- Uses of Killing and Killing-Yano Tensors
- Geodesic motion in the five-dimensional Myers-Perry-AdS spacetime
- Killing-Yano symmetry of Kaluza-Klein black holes in five dimensions
- Hidden Symmetries and Geodesics of Kerr spacetime in Kaluza-Klein Theory
- Deformed and twisted black holes with NUTs
- A Class of Integrable Metrics
- Weak Cosmic Censorship Conjecture in Myers-Perry Black Hole with Separability
- Reducibility of Killing tensors in d>4 NHEK geometry
- Local energy decay of massive Dirac fields in the 5D Myers-Perry metric
- Integrability Conditions for Killing-Yano Tensors and Maximally Symmetric Spaces in the Presence of Torsion
- Conformal bridge in a cosmic string background
- Stationary Spinning Strings and Symmetries of Classical Spacetimes
- Hidden Symmetries and Black Holes
- Separation of variables in the WZW models
- Applications of hidden symmetries to black hole physics
- The precession of particle spin in spherical symmetric spacetimes
- Hidden symmetries and Killing tensors on curved spaces
- Conformally Invariant Spinorial Equations in Six Dimensions
- Coupling constant metamorphosis, Fermat principle and light propagation in Kerr metric
- Killing Spinors and Related Symmetries in Six Dimensions
- Symmetries of modified Dirac operators in supergravity flux backgrounds
- Brane Symmetries Revisited: Symmetries of Tensile and Tensionless Branes in Possibly Degenerate Metrics and their Manifestations
- Higher-dimensional black holes with multiple equal rotations