The large D limit of General Relativity

Abstract

General Relativity simplifies dramatically in the limit that the number of spacetime dimensions D is infinite: it reduces to a theory of non-interacting particles, of finite radius but vanishingly small cross sections, which do not emit nor absorb radiation of any finite frequency. Non-trivial black hole dynamics occurs at length scales that are 1/D times smaller than the horizon radius, and at frequencies D times larger than the inverse of this radius. This separation of scales at large D, which is due to the large gradient of the gravitational potential near the horizon, allows an effective theory of black hole dynamics. We develop to leading order in 1/D this effective description for massless scalar fields and compute analytically the scalar absorption probability. We solve to next-to-next-to-leading order the black brane instability, with very accurate results that improve on previous approximations with other methods. These examples demonstrate that problems that can be formulated in an arbitrary number of dimensions may be tractable in analytic form, and very efficiently so, in the large D expansion.

50 pages, 2 figures; v3: improved discussion of conceptual points

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• Black Strings, Low Viscosity Fluids, and Violation of Cosmic Censorship
• Black Holes as Lumps of Fluid
• High and Low Dimensions in The Black Hole Negative Mode
• AdS/Ricci-flat correspondence and the Gregory-Laflamme instability
• Kaluza-Klein theory in the limit of large number of extra dimensions
• Radiation from a D-dimensional collision of shock waves: higher order set up and perturbation theory validity
• Hyperentropic systems and the generalized second law of thermodynamics
• Quantum buoyancy, generalized second law, and higher-dimensional entropy bounds
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Cited by in corpus (153)

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