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The large D limit of General Relativity

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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.

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Authors and Affiliations

  1. Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig Lluís Companys 23, E-08010, Barcelona, Spain

    Roberto Emparan

  2. Departament de Física Fonamental, Institut de Ciències del Cosmos, Universitat de Barcelona, Martí i Franquès 1, E-08028, Barcelona, Spain

    Roberto Emparan & Kentaro Tanabe

  3. Department of Physics, Kyoto University, Kyoto, 606-8502, Japan

    Ryotaku Suzuki

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  1. Roberto Emparan
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  2. Ryotaku Suzuki
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  3. Kentaro Tanabe
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Correspondence to Roberto Emparan.

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ArXiv ePrint: 1302.6382

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Emparan, R., Suzuki, R. & Tanabe, K. The large D limit of General Relativity. J. High Energ. Phys. 2013, 9 (2013). https://doi.org/10.1007/JHEP06(2013)009

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