Effective theory of black holes in the 1/D expansion

  • Roberto EmparanEmail author
  • Tetsuya Shiromizu
  • Ryotaku Suzuki
  • Kentaro Tanabe
  • Takahiro Tanaka
Open Access
Regular Article - Theoretical Physics


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 (e.g. 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’, i.e. black holes localized at the boundary of AdS, and for non-uniform black strings.


Black Holes Classical Theories of Gravity Black Holes in String Theory 


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© The Author(s) 2015

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Roberto Emparan
    • 1
    • 2
    Email author
  • Tetsuya Shiromizu
    • 3
    • 4
  • Ryotaku Suzuki
    • 5
  • Kentaro Tanabe
    • 6
  • Takahiro Tanaka
    • 7
    • 8
  1. 1.Institució Catalana de Recerca i Estudis Avançats (ICREA)BarcelonaSpain
  2. 2.Departament de F´ısica Fonamental, Institut de Ciències del CosmosUniversitat de BarcelonaBarcelonaSpain
  3. 3.Department of MathematicsNagoya UniversityNagoyaJapan
  4. 4.Kobayashi-Maskawa InstituteNagoya UniversityNagoyaJapan
  5. 5.Department of PhysicsOsaka City UniversityOsakaJapan
  6. 6.Theory Center, Institute of Particles and Nuclear Studies, KEKTsukubaJapan
  7. 7.Department of PhysicsKyoto UniversityKyotoJapan
  8. 8.Yukawa Institute for Theoretical PhysicsKyoto UniversityKyotoJapan

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