Hidden Symmetry of Higher Dimensional Kerr-NUT-AdS Spacetimes

Abstract

It is well known that 4-dimensional Kerr-NUT-AdS spacetime possesses the hidden symmetry associated with the Killing-Yano tensor. This tensor is "universal" in the sense that there exist coordinates where it does not depend on any of the free parameters of the metric. Recently the general higher dimensional Kerr-NUT-AdS solutions of the Einstein equations were obtained. We demonstrate that all these metrics with arbitrary rotation and NUT parameters admit a universal Killing-Yano tensor. We give an explicit presentation of the Killing-Yano and Killing tensors and briefly discuss their properties.

4 pages, some discussion and references are added

References in corpus (5)

• General Kerr-NUT-AdS Metrics in All Dimensions
• Separability of the Hamilton-Jacobi and Klein-Gordon Equations in Kerr-de Sitter Metrics
• Particle Motion and Scalar Field Propagation in Myers-Perry Black Hole Spacetimes in All Dimensions
• A Killing tensor for higher dimensional Kerr-AdS black holes with NUT charge
• Separability in Cohomogeneity-2 Kerr-NUT-AdS Metrics

Cited by in corpus (54)

• Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
• Hidden symmetries, null geodesics, and photon capture in the Sen black hole
• 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
• Higher-Dimensional Black Holes: Hidden Symmetries and Separation of Variables
• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Closed conformal Killing-Yano tensor and Kerr-NUT-de Sitter spacetime uniqueness
• Separability of Dirac equation in higher dimensional Kerr-NUT-de Sitter spacetime
• On conformal Killing-Yano tensors for Plebanski-Demianski family of solutions
• Constants of Geodesic Motion in Higher-Dimensional Black-Hole Spacetimes
• Charged particle in higher dimensional weakly charged rotating black hole spacetime
• Generalized hidden symmetries and the Kerr-Sen black hole
• Complete Set of Commuting Symmetry Operators for the Klein-Gordon Equation in Generalized Higher-Dimensional Kerr-NUT-(A)dS Spacetimes
• Closed conformal Killing-Yano tensor and geodesic integrability
• Commuting symmetry operators of the Dirac equation, Killing-Yano and Schouten-Nijenhuis brackets
• Closed conformal Killing-Yano tensor and uniqueness of generalized Kerr-NUT-de Sitter spacetime
• Stationary strings and branes in the higher-dimensional Kerr-NUT-(A)dS spacetimes
• Unfolded Description of $Ad{S}_4$ Kerr Black Hole
• A Note on Separability of Field Equations in Myers-Perry Spacetimes
• Love Numbers for Rotating Black Holes in Higher Dimensions
• Generalized Kerr-NUT-de Sitter metrics in all dimensions
• Dynamics of test particles in the general five-dimensional Myers-Perry spacetime
• Electromagnetic Field in Higher-Dimensional Black-Hole Spacetimes
• 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
• Geodesic Motion in the Singly Spinning Black Ring Spacetime
• On the parameters of the Kerr-NUT-(anti-)de Sitter space-time
• Aligned Fields Double Copy to Kerr-NUT-(A)dS
• Parallel-propagated frame along null geodesics in higher-dimensional black hole spacetimes
• Hidden symmetries of Eisenhart-Duval lift metrics and the Dirac equation with flux
• Constants of Motion for Constrained Hamiltonian Systems: A Particle around a Charged Rotating Black Hole
• Geodesic Motion in the (Charged) Doubly Spinning Black Ring Spacetime
• Solving parallel transport equations in the higher-dimensional Kerr-NUT-(A)dS spacetimes
• Do Killing-Yano tensors form a Lie Algebra?
• Symmetry operators and separability of massive Klein-Gordon and Dirac equations in the general 5-dimensional Kerr-(anti-)de Sitter black hole background
• Stationary Strings in the Spacetime of Rotating Black Holes in Five-Dimensional Minimal Gauged Supergravity
• Weak electromagnetic field admitting integrability in Kerr-NUT-(A)dS spacetimes
• On hidden symmetries of extremal Kerr-NUT-AdS-dS black holes
• SUSY in the Spacetime of Higher-Dimensional Rotating Black Holes
• Weakly charged generalized Kerr-NUT-(A)dS spacetimes
• Uniqueness of Rotating Charged Black Holes in Five-Dimensional Minimal Gauged Supergravity
• Black hole photon ring beyond General Relativity: an integrable parametrization
• Integrability of geodesic motions in curved manifolds through non-local conserved charges
• Electric/magnetic duality of dyonic Kerr-Newman-NUT-AdS spacetimes
• Ray-tracing in four and higher dimensional black holes: An analytical approximation
• Hidden Conformal Symmetries from Killing Towers with an Application to Large-D/CFT
• The curvature of almost Robinson manifolds
• CFT Duals for Black Rings and Black Strings
• Hidden Symmetries of the Dirac equation in curved spacetime
• Homogeneous Symmetry Operators in Kerr--NUT--AdS Spacetimes
• On a lower-dimensional Killing vector origin of irreducible Killing tensors
• Hyperelliptic functions and motion in general relativity
• Higher-dimensional black holes with multiple equal rotations
• Report on workshop A1: Exact solutions and their interpretation