Gravitational Perturbations of Higher Dimensional Rotating Black Holes: Tensor Perturbations

Abstract

Assessing the stability of higher-dimensional rotating black holes requires a study of linearized gravitational perturbations around such backgrounds. We study perturbations of Myers-Perry black holes with equal angular momenta in an odd number of dimensions (greater than five), allowing for a cosmological constant. We find a class of perturbations for which the equations of motion reduce to a single radial equation. In the asymptotically flat case we find no evidence of any instability. In the asymptotically anti-de Sitter case, we demonstrate the existence of a superradiant instability that sets in precisely when the angular velocity of the black hole exceeds the speed of light from the point of view of the conformal boundary. We suggest that the endpoint of the instability may be a stationary, nonaxisymmetric black hole.

arXiv commentlatex, 29 pages, 5 figures. v2 reference added. v3 title changed, note added on classification of perturbations (this paper deals with the most general tensor perturbations)

References in corpus (39)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Black Strings and p-Branes are Unstable
• A rotating black ring in five dimensions
• All supersymmetric solutions of minimal supergravity in five dimensions
• Rotation and the AdS/CFT correspondence
• The First Law of Thermodynamics for Kerr-Anti-de Sitter Black Holes
• The General Kerr-de Sitter Metrics in All Dimensions
• A master equation for gravitational perturbations of maximally symmetric black holes in higher dimensions
• General supersymmetric AdS5 black holes
• General Non-Extremal Rotating Black Holes in Minimal Five-Dimensional Gauged Supergravity
• The black hole bomb and superradiant instabilities
• Rotating Black Holes in Higher Dimensions with a Cosmological Constant
• The evolution of unstable black holes in anti-de Sitter space
• Supersymmetric AdS5 black holes
• A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric
• Stability of Higher-Dimensional Schwarzschild Black Holes
• Charged and rotating AdS black holes and their CFT duals
• Static Axisymmetric Vacuum Solutions and Non-Uniform Black Strings
• Instability of Ultra-Spinning Black Holes
• Small Kerr-anti-de Sitter black holes are unstable
• On non-uniform black branes
• Higher dimensional black holes and supersymmetry
• Supersymmetric multi-charge AdS_5 black holes
• Fate of the Black String Instability
• Classical and Thermodynamic Stability of Black Branes
• Quantum Radiation from a 5-Dimensional Rotating Black Hole
• Gravitational instability in higher dimensions
• Five-Dimensional Gauged Supergravity Black Holes with Independent Rotation Parameters
• Superradiant instabilities of rotating black branes and strings
• All supersymmetric solutions of minimal gauged supergravity in five dimensions
• Kaluza-Klein Consistency, Killing Vectors, and Kahler Spaces
• Separability of the Hamilton-Jacobi and Klein-Gordon Equations in Kerr-de Sitter Metrics
• The scalar perturbation of the higher-dimensional rotating black holes
• 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
• Integrability of Particle Motion and Scalar Field Propagation in Kerr-(Anti) de Sitter Black Hole Spacetimes in All Dimensions
• Scalar perturbations of higher dimensional rotating and ultra-spinning black holes
• Scalar field perturbation on six-dimensional ultra-spinning black holes

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