Unstable `black branes' from scaled membranes at large $D$

Abstract

It has recently been demonstrated that the dynamics of black holes at large $D$ can be recast as a set of non gravitational membrane equations. These membrane equations admit a simple static solution with shape $S^{D-p-2}\times R^{p,1}$. In this note we study the equations for small fluctuations about this solution in a limit in which amplitude and length scale of the fluctuations are simultaneously scaled to zero as $D$ is taken to infinity. We demonstrate that the resultant nonlinear equations, which capture the Gregory- Laflamme instability and its end point, exactly agree with the effective dynamical `black brane' equations of Emparan Suzuki and Tanabe. Our results thus identify the `black brane' equations as a special limit of the membrane equations and so unify these approaches to large $D$ black hole dynamics.

arXiv comment10 pages, references added

References in corpus (16)

• The large D limit of General Relativity
• Large D gravity and low D strings
• The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity
• Effective theory of Black Holes in the 1/D expansion
• Evolution and endpoint of the black string instability: Large D solution
• Decoupling and non-decoupling dynamics of large D black holes
• Quasinormal modes of (Anti-)de Sitter black holes in the 1/D expansion
• Hydro-elastic Complementarity in Black Branes at large D
• Black Brane Viscosity and the Gregory-Laflamme Instability
• Instability of rotating black holes: large D analysis
• 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
• Quasinormal modes of Gauss-Bonnet black holes at large D
• Black rings at large D
• Holographic superconductivity in the large D expansion
• On Brane Instabilities in the Large $D$ Limit

Cited by in corpus (29)

• The Large D Limit of Einstein's Equations
• Currents and Radiation from the large $D$ Black Hole Membrane
• Phases and Stability of Non-Uniform Black Strings
• Einstein-Gauss-Bonnet Black Strings at Large $D$
• Rotating black holes and black bars at large D
• 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 $D$
• Charged Black Rings at large D
• Holographic duals of evaporating black holes
• The large D black hole dynamics in AdS/dS backgrounds
• Black holes in presence of cosmological constant: Second order in 1/D
• Holographic Bjorken Flow at Large-D
• Black Tsunamis and Naked Singularities in AdS
• The Large Dimension Limit of a Small Black Hole Instability in Anti-de Sitter Space
• Large D holography with metric deformations
• 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 $D$
• Entropy production and entropic attractors in black hole fusion and fission
• The large D Membrane Paradigm For Einstein-Gauss-Bonnet Gravity
• A leading-order comparison between fluid-gravity and membrane-gravity dualities
• The large $D$ membrane paradigm for general four-derivative theory of gravity with a cosmological constant
• Fluid-gravity and membrane-gravity dualities - Comparison at subleading orders
• Black Rings in Large $D$ Membrane Paradigm at the First Order
• General Theory of Large D Membranes Consistent with Second Law of Thermodynamics
• Study of Semiclassical Instability of the Schwarzschild AdS Black Hole in the Large $D$ Limit
• Stress Tensor for Large-$D$ membrane at subleading orders
• An analytic approach for holographic entanglement entropy at (quantum) criticality