The Large D Limit of Einstein's Equations

2020/03/25 by Roberto Emparan, Christopher P. Herzog
Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal map #Cosmology and Gravitation Theories #Einstein #Geometry #Limit (mathematics) #Mathematical analysis #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Statistical mechanics #gr-qc #hep-th

paper · pdf · doi:10.1103/revmodphys.92.045005

published as Rev. Mod. Phys. 92, 45005 (2020) · 59 pages, 10 figures; formatted for submission as a review to RMP; please send us feedback

arxiv created 2020/03/25 · openalex created_date 2020/04/03 · openalex publication_date 2020/11/18 · arxiv updated 2022/03/07 · openalex updated_date 2026/08/05

Abstract

We review recent progress in taking the large dimension limit of Einstein's equations. Most of our analysis is classical in nature and concerns situations where there is a black hole horizon although we briefly discuss various extensions that include quantum gravitational effects. The review consists of two main parts: the first a discussion of general aspects of black holes and effective membrane theories in this large dimension limit, and the second a series of applications of this limit to interesting physical problems. The first part includes a discussion of quasinormal modes which leads naturally into a description of effective hydrodynamic-like 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 we discuss in relation to each other. In the second part we divide the applications 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 us to extend our spectrum of applications to problems in hydrodynamics, condensed matter physics, and nuclear physics. A final, shorter part of the review describes further promising directions where there have been, as yet, few published research articles.

Citations

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• Comments on the Sachdev-Ye-Kitaev model
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• The large dimension limit of a small black hole instability in anti-de Sitter space
• Gravitating Scalars and Critical Collapse in the Large D Limit
• Models of AdS₂ Backreaction and Holography
• Comparison between fluid-gravity and membrane-gravity dualities for Einstein-Maxwell system