Instability of rotating black holes: large D analysis

Abstract

We study the stability of odd-dimensional rotating black holes with equal angular momenta by performing an expansion in the inverse of the number of dimensions D. Universality at large $D$ allows us to calculate analytically the complex frequency of quasinormal modes to next-to-leading order in the expansion. We identify the onset of non-axisymmetric, bar-mode instabilities at a specific finite rotation, and axisymmetric instabilities at larger rotation. The former occur at the threshold where the modes become superradiant, and before the ultraspinning regime is reached. Our results fully confirm the picture found in numerical studies, with very good quantitative agreement. We extend the analysis to the same class of black holes in Anti-deSitter space, and find the same qualitative features. We also discuss the appearance at high frequencies of the universal set of (stable) quasinormal modes.

38 pages, 14 figures. v3: NLO results included so the instability is shown to occur before the ultraspinning regime of rotation. Significant improvements in accuracy. Ancillary Mathematica notebook contains details of NLO results

References in corpus (4)

• An instability of higher-dimensional rotating black holes
• Holographic thermalization, quasinormal modes and superradiance in Kerr-AdS
• High and Low Dimensions in The Black Hole Negative Mode
• Stability of Five-dimensional Myers-Perry Black Holes with Equal Angular Momenta

Cited by in corpus (39)

• Numerical Methods for Finding Stationary Gravitational Solutions
• Phase Diagram of Planar Matrix Quantum Mechanics, Tensor, and Sachdev-Ye-Kitaev Models
• Effective theory of Black Holes in the 1/D expansion
• Decoupling and non-decoupling dynamics of large D black holes
• Exploring New Physics Frontiers Through Numerical Relativity
• A membrane paradigm at large D
• Quasinormal modes of (Anti-)de Sitter black holes in the 1/D expansion
• The holographic dual of a Riemann problem in a large number of dimensions
• Non-uniform black strings and the critical dimension in the $1/D$ expansion
• The large D black hole Membrane Paradigm at first subleading order
• Currents and Radiation from the large $D$ Black Hole Membrane
• Quasinormal modes of Gauss-Bonnet black holes at large D
• Black rings at large D
• Unstable `black branes' from scaled membranes at large $D$
• Rotating black holes and black bars at large D
• More on the New Large $D$ Limit of Matrix Models
• Holographic Turbulence in a Large Number of Dimensions
• An Action for and Hydrodynamics from the improved Large D membrane
• Static Gauss-Bonnet Black Holes at Large $D$
• A Charged Membrane Paradigm at Large D
• Charged Black Rings at large D
• The large D black hole dynamics in AdS/dS backgrounds
• Black holes in presence of cosmological constant: Second order in 1/D
• Einstein-Gauss-Bonnet Black Rings at Large $D$
• The Large Dimension Limit of a Small Black Hole Instability in Anti-de Sitter Space
• Large D gravity and charged membrane dynamics with nonzero cosmological constant
• Stationary Solutions from the Large D Membrane Paradigm
• Holographic Turbulence in Einstein-Gauss-Bonnet Gravity at Large $D$
• Photon Emission Near Myers-Perry Black Holes in the Large Dimension Limit
• Black Ripples, Flowers and Dumbbells at large $D$
• Non-spherically symmetric black string perturbations in the large D limit
• The large $D$ membrane paradigm for general four-derivative theory of gravity with a cosmological constant
• Cosmic Censorship at Large D: Stability analysis in polarized AdS black branes (holes)
• Black Rings in Large $D$ Membrane Paradigm at the First Order
• Rotating black holes at large $D$ in Einstein-Gauss-Bonnet theory
• Horizon Tunneling Revisited: The Case of Higher Dimensional Black Holes
• Black hole one-loop determinants in the large dimension limit
• Study of Semiclassical Instability of the Schwarzschild AdS Black Hole in the Large $D$ Limit
• Stress Tensor for Large-$D$ membrane at subleading orders