Study of Semiclassical Instability of the Schwarzschild AdS Black Hole in the Large $D$ Limit

Abstract

We analyze the semiclassical stability of the Schwarzschild AdS black hole in the Euclidean partition function approach. We perform this computation in the large $D$ limit and focus on scalar perturbations. We obtain the equations for non-spherically symmetric scalar perturbations in a simple form. For a class of perturbations stability is demonstrated by the S-deformation method. For some other classes we rule out unstable modes of $\mathcal{O}(D^2)$. We also analyze the spherically symmetric perturbations and demonstrate the appearance of an unstable mode for small black holes in the large $D$ limit. We obtain an expression for the eigenvalue corresponding to the unstable mode to next to leading order in a $1/D$ expansion. This result agrees with a previously obtained numerical bound on this eigenvalue. For cosmological constant zero, our answer matches a previous result obtained for the corresponding eigenvalue for the $D$ dimensional Schwarzschild-Tangherlini black hole to next to leading order in a $1/D$ expansion.

arXiv comment41 pages, cut-paste typos in pedagogical Appendix fixed, no changes to results or in main body of paper, supercedes journal version

References in corpus (39)

• Black Strings and p-Branes are Unstable
• A master equation for gravitational perturbations of maximally symmetric black holes in higher dimensions
• Brane World Cosmology - Gauge-Invariant Formalism for Perturbation
• Dynamics in Non-Globally-Hyperbolic Static Spacetimes III: Anti-de Sitter Spacetime
• The large D limit of General Relativity
• Large D gravity and low D strings
• Dynamic and Thermodynamic Stability and Negative Modes in Schwarzschild-Anti-de Sitter
• Effective theory of Black Holes in the 1/D expansion
• Evolution and endpoint of the black string instability: Large D solution
• Perturbations and Stability of Static Black Holes in Higher Dimensions
• On Black-Brane Instability In an Arbitrary Dimension
• Decoupling and non-decoupling dynamics of large D black holes
• A membrane paradigm at large D
• Universal quasinormal modes of large D black holes
• High and Low Dimensions in The Black Hole Negative Mode
• Quasinormal modes of (Anti-)de Sitter black holes in the 1/D expansion
• Hydro-elastic Complementarity in Black Branes at large D
• Instability of rotating black holes: large D analysis
• 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
• Phases and Stability of Non-Uniform Black Strings
• Quasinormal modes of Gauss-Bonnet black holes at large D
• Instability of de Sitter Reissner-Nordstrom black hole in the 1/D expansion
• Einstein-Gauss-Bonnet Black Strings at Large $D$
• Black rings at large D
• Unstable `black branes' from scaled membranes at large $D$
• 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
• The Power of Action: "The" Derivation of the Black Hole Negative Mode
• 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 $D$
• Large D gravity and charged membrane dynamics with nonzero cosmological constant
• Stability analysis of black holes by the $S$-deformation method for coupled systems
• Non-spherically symmetric black string perturbations in the large D limit
• The large D Membrane Paradigm For Einstein-Gauss-Bonnet Gravity

Cited by in corpus (2)

• Quantum Thermodynamics of a Quantum Sized AdS Black Hole
• Black Rings in Large $D$ Membrane Paradigm at the First Order