Non-spherically symmetric black string perturbations in the large D limit

Abstract

We consider non-spherically symmetric perturbations of the uncharged black string/flat black brane in the large dimension (D) limit of general relativity. We express the perturbations in a simplified form using variables introduced by Ishibashi and Kodama. We apply the large D limit to the equations, and show that this leads to decoupling of the equations in the near-horizon and asymptotic regions. It also enables use of matched asymptotic expansions to obtain approximate analytical solutions and to analyze stability of the black string/brane. For a large class of non-spherically symmetric perturbations, we prove that there are no instabilities in the large D limit. For the rest, we provide additional matching arguments that indicate that the black string/brane is stable. In the \emph{static} limit, we show that for \emph{all} non-spherically symmetric perturbations, there is no instability. This is proof that the Gross-Perry-Yaffe mode for semiclassical black hole perturbations is the unique unstable mode even in the large D limit. This work is also a direct analytical indication that the only instability of the black string is the Gregory-Laflamme instability.

arXiv comment44 pages, two references added, version accepted for publication in Physical Review D

References in corpus (39)

• Quasinormal modes of black holes and black branes
• Black Strings and p-Branes are Unstable
• Quasinormal modes and holography
• A master equation for gravitational perturbations of maximally symmetric black holes in higher dimensions
• The evolution of unstable black holes in anti-de Sitter space
• Brane World Cosmology - Gauge-Invariant Formalism for Perturbation
• Quasinormal Modes of Near Extremal Black Branes
• The large D limit of General Relativity
• Classical and Thermodynamic Stability of Black Branes
• The Phase Transition between Caged Black Holes and Black Strings - A Review
• Gravitational instability in higher dimensions
• Instabilities of Black Strings and Branes
• Instability of charged black holes in anti-de Sitter space
• Large D gravity and low D strings
• Rayleigh-Plateau and Gregory-Laflamme instabilities of black strings
• 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
• Black Rings, Boosted Strings and Gregory-Laflamme
• 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 D-dimensional extremally charged Reissner-Nordstrom(-de Sitter) black holes: Extrapolation to arbitrary D
• Instability of rotating black holes: large D analysis
• Quasinormal modes of asymptotically flat rotating black holes
• Non-uniform black strings and the critical dimension in the $1/D$ expansion
• Looking at the Gregory-Laflamme instability through quasi-normal modes
• Origin of black string instability
• Quasinormal modes of Gauss-Bonnet black holes at large D
• Instability of de Sitter Reissner-Nordstrom black hole in the 1/D expansion
• Black rings at large D
• Classical Stability of Charged Black Branes and the Gubser-Mitra Conjecture
• Perturbations and Stability of Higher-Dimensional Black Holes
• A Charged Membrane Paradigm at Large D
• Investigating stability of a class of black hole spacetimes under Ricci flow
• Analytic evidence for the Gubser-Mitra conjecture

Cited by in corpus (11)

• Currents and Radiation from the large $D$ Black Hole Membrane
• Einstein-Gauss-Bonnet Black Strings at Large $D$
• An Action for and Hydrodynamics from the improved Large D membrane
• Static Gauss-Bonnet Black Holes at Large $D$
• Black holes in presence of cosmological constant: Second order in 1/D
• Einstein-Gauss-Bonnet Black Rings at Large $D$
• Stationary Solutions from the Large D Membrane Paradigm
• Large D gravity and charged membrane dynamics with nonzero cosmological constant
• Black Rings in Large $D$ Membrane Paradigm at the First Order
• Study of Semiclassical Instability of the Schwarzschild AdS Black Hole in the Large $D$ Limit
• Stress Tensor for Large-$D$ membrane at subleading orders