Integrability of Particle Motion and Scalar Field Propagation in Kerr-(Anti) de Sitter Black Hole Spacetimes in All Dimensions
arXiv:gr-qc/0507096 · doi:10.1103/PhysRevD.72.124008
Abstract
We study the Hamilton-Jacobi and massive Klein-Gordon equations in the general Kerr-(Anti) de Sitter black hole background in all dimensions. Complete separation of both equations is carried out in cases when there are two sets of equal black hole rotation parameters. We analyze explicitly the symmetry properties of these backgrounds that allow for this Liouville integrability and construct a nontrivial irreducible Killing tensor associated with the enlarged symmetry group which permits separation. We also derive first-order equations of motion for particles in these backgrounds and examine some of their properties. This work greatly generalizes previously known results for both the Myers-Perry metrics, and the Kerr-(Anti) de Sitter metrics in higher dimensions.
23 pages, LaTeX2e
References in corpus (9)
- Rotating Black Holes in Higher Dimensions with a Cosmological Constant
- The geodesic structure of the Schwarzschild Anti-de Sitter black hole
- Separability of the Hamilton-Jacobi and Klein-Gordon Equations in Kerr-de Sitter Metrics
- Beyond the veil: Inner horizon instability and holography
- Particle Motion and Scalar Field Propagation in Myers-Perry Black Hole Spacetimes in All Dimensions
- Integrability and the Kerr-(A)dS black hole in five dimensions
- On Charged Black Holes in Anti-de Sitter Space
- Extracting Data from Behind Horizons with the AdS/CFT Correspondence
- Integrability of Some Charged Rotating Supergravity Black Hole Solutions in Four and Five Dimensions
Cited by in corpus (28)
- Black holes, hidden symmetries, and complete integrability
- Gravitational Perturbations of Higher Dimensional Rotating Black Holes: Tensor Perturbations
- Hidden symmetries, null geodesics, and photon capture in the Sen black hole
- BlackMax: A black-hole event generator with rotation, recoil, split branes and brane tension
- Complete Integrability of Geodesic Motion in General Kerr-NUT-AdS Spacetimes
- Separability of Hamilton-Jacobi and Klein-Gordon Equations in General Kerr-NUT-AdS Spacetimes
- `Hidden' Symmetries of Higher Dimensional Rotating Black Holes
- Higher-Dimensional Black Holes: Hidden Symmetries and Separation of Variables
- Hidden Symmetry of Higher Dimensional Kerr-NUT-AdS Spacetimes
- Cosmic Censorship of Rotating Anti-de Sitter Black Hole
- Separation of Maxwell equations in Kerr-NUT-(A)dS spacetimes
- Thermodynamics of Three-dimensional Black Holes via Charged Particle Absorption
- Special symmetries of the charged Kerr-AdS black hole of D=5 minimal gauged supergravity
- 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
- N-dimensional sl(2)-coalgebra spaces with non-constant curvature
- Rotating Black Hole Thermodynamics with a Particle Probe
- Superradiance Instability of Small Rotating AdS Black Holes in Arbitrary Dimensions
- 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 Killing tensor for higher dimensional Kerr-AdS black holes with NUT charge
- Integrability of Some Charged Rotating Supergravity Black Hole Solutions in Four and Five Dimensions
- Constraints on Scalar-Tensor Theory of Gravity by Solar System Tests
- Spacetimes with a separable Klein-Gordon equation in higher dimensions
- N-dimensional integrability from two-photon coalgebra symmetry
- Separability of multi-charge black holes in supergravity
- A Note on Particles and Scalar Fields in Higher Dimensional Nutty Spacetimes
- Angular Eigenvalues of Higher-Dimensional Kerr-(A)dS Black Holes with Two Rotations
- Periapsis shift and deflection of light by hairy black holes