A Killing tensor for higher dimensional Kerr-AdS black holes with NUT charge

Abstract

In this paper, we study the recently discovered family of higher dimensional Kerr-AdS black holes with an extra NUT-like parameter. We show that the inverse metric is additively separable after multiplication by a simple function. This allows us to separate the Hamilton-Jacobi equation, showing that geodesic motion is integrable on this background. The separation of the Hamilton-Jacobi equation is intimately linked to the existence of an irreducible Killing tensor, which provides an extra constant of motion. We also demonstrate that the Klein-Gordon equation for this background is separable.

LaTeX, 14 pages. v2: Typo corrected and equation added. v3: Reference added, introduction expanded, published version

References in corpus (2)

• Separability of the Hamilton-Jacobi and Klein-Gordon Equations in Kerr-de Sitter Metrics
• Integrability and the Kerr-(A)dS black hole in five dimensions

Cited by in corpus (10)

• 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
• `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
• Closed conformal Killing-Yano tensor and uniqueness of generalized Kerr-NUT-de Sitter 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
• Symmetry operators and separability of massive Klein-Gordon and Dirac equations in the general 5-dimensional Kerr-(anti-)de Sitter black hole background
• Separability of multi-charge black holes in supergravity