The Large D Limit of Einstein's Equations

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.

arXiv comment59 pages, 10 figures; formatted for submission as a review to RMP; please send us feedback

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• Hydrodynamic attractors in heavy ion collisions: a review
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• Holographic duals of evaporating black holes
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• Reconstruction of the quasinormal spectrum from pole-skipping
• Black Tsunamis and Naked Singularities in AdS
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• The Swampland at Large Number of Space-Time Dimensions
• Einstein-Gauss-Bonnet black strings at large $\alpha$
• The Hookean Law of Black Holes and Fragmentation: Insights from Maximum Force Conjecture and Ruppeiner Geometry
• Quantum information measures of the Dirichlet and Neumann hyperspherical dots
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• A Zoo of Deformed Jackiw-Teitelboim Models near Large Dimensional Black Holes
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• General Theory of Large D Membranes Consistent with Second Law of Thermodynamics
• Lumos Extrema
• Rotating black holes at large $D$ in Einstein-Gauss-Bonnet theory
• Metric fluctuations in higher-dimensional black holes
• Critical spacetime crystals in continuous dimensions
• The Black hole Black string phase transition in Einstein-Gauss-Bonnet gravity
• Lattice Black Branes at Large $D$
• Phase and stability of black strings in Einstein-Gauss-Bonnet theory at large D
• Hawking radiation from nonrotating singularity-free black holes in conformal gravity
• Squashed black holes at large $D$
• An analytic approach for holographic entanglement entropy at (quantum) criticality
• Numerical Relativity, Holography and the Quantum Null Energy Condition
• Analyzes of Algebraic Classification of Higher Dimensional Kundt Geometries with Large $D$ Method
• If you want to cross singularity, wrap it!
• Toroidal $\&$ orbifold compactifications at large D and D-duality