Effective theory of Black Holes in the 1/D expansion

Abstract

The gravitational field of a black hole is strongly localized near its horizon when the number of dimensions D is very large. In this limit, we can effectively replace the black hole with a surface in a background geometry (eg Minkowski or Anti-deSitter space). The Einstein equations determine the effective equations that this 'black hole surface' (or membrane) must satisfy. We obtain them up to next-to-leading order in 1/D for static black holes of the Einstein-(A)dS theory. To leading order, and also to next order in Minkowski backgrounds, the equations of the effective theory are the same as soap-film equations, possibly up to a redshift factor. In particular, the Schwarzschild black hole is recovered as a spherical soap bubble. Less trivially, we find solutions for 'black droplets', ie black holes localized at the boundary of AdS, and for non-uniform black strings.

32 pages, 3 figures

References in corpus (11)

• Nonlinear Fluid Dynamics from Gravity
• A membrane paradigm at large D
• High and Low Dimensions in The Black Hole Negative Mode
• Quasinormal modes of (Anti-)de Sitter black holes in the 1/D expansion
• New nonuniform black string solutions
• Nonuniform black strings in various dimensions
• AdS flowing black funnels: Stationary AdS black holes with non-Killing horizons and heat transport in the dual CFT
• Stable non-uniform black strings below the critical dimension
• Non-uniform black strings and the critical dimension in the $1/D$ expansion
• Black Droplets
• Stationary black holes: Large $D$ analysis

Cited by in corpus (65)

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• Instability of de Sitter Reissner-Nordstrom black hole in the 1/D expansion
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• Einstein-Gauss-Bonnet Black Strings at Large $D$
• Unstable `black branes' from scaled membranes at large $D$
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• Charged rotating black holes in higher dimensions
• Holographic Turbulence in a Large Number of Dimensions
• More on the New Large $D$ Limit of Matrix Models
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• Static Gauss-Bonnet Black Holes at Large $D$
• A Charged Membrane Paradigm at Large D
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• The large D black hole dynamics in AdS/dS backgrounds
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• Stationary Solutions from the Large D Membrane Paradigm
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• Holographic Turbulence in Einstein-Gauss-Bonnet Gravity at Large $D$
• Topology-changing horizons at large D as Ricci flows
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• General Theory of Large D Membranes Consistent with Second Law of Thermodynamics
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