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.

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

References in corpus (41)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Building an AdS/CFT superconductor
• Nonlinear Fluid Dynamics from Gravity
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Black Strings, Low Viscosity Fluids, and Violation of Cosmic Censorship
• Thermoelectric DC conductivities from black hole horizons
• Universal hydrodynamics of non-conformal branes
• An Analytic Holographic Superconductor
• Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions
• Numerical Relativity and Astrophysics
• Well-posed formulation of Lovelock and Horndeski theories
• Classical instability of Kerr-AdS black holes and the issue of final state
• Rayleigh-Plateau and Gregory-Laflamme instabilities of black strings
• Causality and Hyperbolicity of Lovelock Theories
• Ultraspinning instability of rotating black holes
• Black Holes as Lumps of Fluid
• High and Low Dimensions in The Black Hole Negative Mode
• Numerical relativity for D dimensional space-times: head-on collisions of black holes and gravitational wave extraction
• The Black Ring is Unstable
• Stable non-uniform black strings below the critical dimension
• AdS/Ricci-flat correspondence and the Gregory-Laflamme instability
• The large D black hole Membrane Paradigm at first subleading order
• Phases Of Melonic Quantum Mechanics
• Lumpy AdS${}_5\times$ S${}^5$ Black Holes and Black Belts
• Einstein-Gauss-Bonnet Black Strings at Large $D$
• Unstable `black branes' from scaled membranes at large $D$
• On Brane Instabilities in the Large $D$ Limit
• Radiation from a D-dimensional collision of shock waves: first order perturbation theory
• Up to eleven: radiation from particles with arbitrary energy falling into higher-dimensional black holes
• Photon Emission Near Myers-Perry Black Holes in the Large Dimension Limit
• Black-hole head-on collisions in higher dimensions
• Kaluza-Klein theory in the limit of large number of extra dimensions
• On the large $D$ expansion of Hermitian multi-matrix models
• Instability of Charged Gauss-Bonnet Black Hole in de Sitter Spacetime at Large $D$
• Black Ripples, Flowers and Dumbbells at large $D$
• Radiation from a D-dimensional collision of shock waves: higher order set up and perturbation theory validity
• Heavy Quark Potential from Gauge/Gravity Duality: A Large D Analysis
• The Fate of Instability of de Sitter Black Holes at Large $D$
• Fluid-gravity and membrane-gravity dualities - Comparison at subleading orders
• Instabilities of Thin Black Rings: Closing the Gap
• Comparison between fluid-gravity and membrane-gravity dualities for Einstein-Maxwell system

Cited by in corpus (35)

• Hydrodynamic attractors in heavy ion collisions: a review
• Hawking evaporation of Einstein-Gauss-Bonnet AdS black holes in $D⩾4$ dimensions
• Holographic duals of evaporating black holes
• Thermal one point functions, large $d$ and interior geometry of black holes
• Reconstruction of the quasinormal spectrum from pole-skipping
• Black Tsunamis and Naked Singularities in AdS
• Island of Reissner-Nordstr$\ddot{\mathbf{o}}$m anti-de Sitter black holes in the large $d$ limit
• 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
• Double scaling limit of multi-matrix models at large $D$
• A Zoo of Deformed Jackiw-Teitelboim Models near Large Dimensional Black Holes
• The large D effective theory of black strings in AdS
• Analytic long-lived modes in charged critical plasma
• Hidden Conformal Symmetries from Killing Towers with an Application to Large-D/CFT
• Black Rings in Large $D$ Membrane Paradigm at the First Order
• Black hole interactions at large $D$: brane blobology
• Generalized dilaton gravity in 2d
• Black Hole Critical Collapse in Infinite Dimensions: Continuous Self-Similar Solutions
• 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