The large D black hole Membrane Paradigm at first subleading order

Abstract

In the large D limit, and under certain circumstances, it has recently been demonstrated that black hole dynamics in asymptotically flat spacetime reduces to the dynamics of a non gravitational membrane propagating in flat D dimensional spacetime. We demonstrate that this correspondence extends to all orders in a 1/D expansion and outline a systematic method for deriving the corrected membrane equation in a power series expansion in 1/D. As an illustration of our method we determine the first subleading corrections to the membrane equations of motion. A qualitatively new effect at this order is that the divergence of the membrane velocity is nonzero and proportional to the square of the shear tensor reminiscent of the entropy current of hydrodynamics. As a test, we use our modified membrane equations to compute the corrections to frequencies of light quasinormal modes about the Schwarzschild black hole and find a perfect match with earlier computations performed directly in the gravitational bulk.

arXiv commentTypesetting corrected, New appendix added to explain the method of computation

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Cited by in corpus (33)

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• 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
• The large D black hole dynamics in AdS/dS backgrounds
• Black holes in presence of cosmological constant: Second order in 1/D
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• 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 holography with metric deformations
• Stationary Solutions from the Large D Membrane Paradigm
• Large D gravity and charged membrane dynamics with nonzero cosmological constant
• Holographic Turbulence in Einstein-Gauss-Bonnet Gravity at Large $D$
• Holographic Observables at Large $d$
• The large D Membrane Paradigm For Einstein-Gauss-Bonnet Gravity
• A leading-order comparison between fluid-gravity and membrane-gravity dualities
• Large D membrane for Higher Derivative Gravity and Black Hole Second Law
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• Fluid-gravity and membrane-gravity dualities - Comparison at subleading orders
• The Fate of Instability of de Sitter Black Holes at Large $D$
• Hidden Conformal Symmetries from Killing Towers with an Application to Large-D/CFT
• Black Rings in Large $D$ Membrane Paradigm at the First Order
• General Theory of Large D Membranes Consistent with Second Law of Thermodynamics
• Horizon Tunneling Revisited: The Case of Higher Dimensional Black Holes
• Study of Semiclassical Instability of the Schwarzschild AdS Black Hole in the Large $D$ Limit
• Black hole one-loop determinants in the large dimension limit
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