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Large D limit of Einstein’s equations

Roberto Emparan* and Christopher P. Herzog†

Roberto Emparan*

  • Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos, Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain and Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig Lluís Companys 23, E-08010 Barcelona, Spain

Christopher P. Herzog†

  • King’s College London, The Strand, London WC2R 2LS, England

  • *emparan@ub.edu
  • †christopher.herzog@kcl.ac.uk
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Rev. Mod. Phys. 92, 045005 – Published 18 November, 2020

DOI: https://doi.org/10.1103/RevModPhys.92.045005

Abstract

Recent progress in taking the large dimension limit of Einstein’s equations is reviewed. Most of the analysis is classical and concerns situations where there is a black hole horizon, although various extensions that include quantum gravitational effects are discussed. The review consists of two main parts: the first is a discussion of general aspects of black holes and effective membrane theories in this large dimension limit, and the second is a series of applications of this limit to interesting physical problems. The first part includes a discussion of quasinormal modes that leads naturally into a description of effective hydrodynamiclike equations that describe the near-horizon geometry. There are two main approaches to these effective theories, a fully covariant approach and a partially gauge-fixed one, which are discussed in relation to each other. In the second part the applications are divided up into three main categories: the Gregory-Laflamme instability, black hole collisions and mergers, and the anti–de Sitter/conformal field theory correspondence (AdS/CFT). AdS/CFT posits an equivalence between a gravitational theory and a strongly interacting field theory, allowing the spectrum of applications to be extended to problems in hydrodynamics, condensed matter physics, and nuclear physics. The final, shorter part of the review describes further promising directions where there have been, as yet, few published research articles.

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Rev. Mod. Phys. 92, 045005– Published 18 November, 2020
  • Received 25 March 2020
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