This article was accepted into the corpus but its outbound wikilinks were never NER-processed — typical at the deepest BFS hop or when the run's entity cap was reached. No expansion funnel to show.
| anti-de Sitter | |
|---|---|
| Name | anti-de Sitter |
| Type | spacetime |
| Dimension | variable |
| Curvature | negative |
| Symmetry | maximal |
anti-de Sitter is a maximally symmetric, vacuum solution of the Einstein field equations with constant negative scalar curvature that plays a central role in modern mathematical physics, string theory, and studies of quantum gravity. It serves as the canonical model of a spacetime with negative cosmological constant and appears in analyses involving the Schwarzschild–AdS metric, Kerr–AdS metric, and in the formulation of the AdS/CFT correspondence. Key figures associated with its development include Albert Einstein, David Hilbert, Roy Kerr, Stephen Hawking, and Juan Maldacena.
The spacetime is defined as the maximally symmetric, simply connected Lorentzian manifold with constant negative curvature, which can be constructed as a hyperboloid embedded in a higher-dimensional flat space with signature (2,n). Important mathematical contributors include Bernhard Riemann, Élie Cartan, Hermann Weyl, Felix Klein, and Élie-Jacques Cartan. Physically relevant parameters are the AdS radius (often denoted ℓ), the negative cosmological constant introduced by Albert Einstein and further studied by Willem de Sitter and Alexander Friedmann, and the spacetime dimension which ranges in studies from 3 to 11 dimensions in works by Edward Witten, Michael Green, John Schwarz, and Cumrun Vafa. The manifold admits global timelike Killing vectors discussed in research by Roger Penrose and Stephen Hawking and supports asymptotically AdS boundary conditions used by James York, Gary Gibbons, and Robert Wald.
The metric of the spacetime can be written in several coordinate systems, including global coordinates, Poincaré coordinates, and static coordinates, as developed in literature by Kip Thorne, Subrahmanyan Chandrasekhar, Jerzy Plebański, and Malcolm Perry. In global coordinates the line element exhibits an explicit dependence on the AdS radius ℓ, while Poincaré coordinates make manifest the conformal boundary studied in work by Paul Dirac, Hermann Minkowski, Roger Penrose, and Israel Gelfand. The curvature tensors, Ricci scalar, and Riemann tensor for the spacetime were computed in classical treatments by Élie Cartan and appear in solutions like the Banados–Teitelboim–Zanelli black hole explored by Maximo Banados, Claudio Teitelboim, and Jorge Zanelli.
Anti-de Sitter spacetime has the maximal isometry group SO(2,n) in n+1 dimensions, a symmetry algebra analyzed by Sophus Lie, Wilhelm Killing, Élie Cartan, and exploited in physics by Hugh Osborn, Daniel Friedan, Joseph Polchinski, and Edward Witten. The presence of conformal symmetry at the boundary relates these isometries to the conformal group of one lower dimension, an observation central to the work of Gerard 't Hooft, Alexander Polyakov, Kenneth Wilson, and Geoffrey Moore. Representations of the isometry algebra are studied through techniques developed by Eugene Wigner, Harish-Chandra, I.M. Gelfand, and Vladimir Drinfeld.
The causal structure features a timelike conformal boundary and closed timelike curves in certain quotients, themes investigated by Roger Penrose, Stephen Hawking, Graham Ellis, and George F. R. Ellis. Global hyperbolicity issues and the role of reflective boundary conditions were explored in contexts by Yvonne Choquet-Bruhat, James York, Gary Gibbons, and Robert Wald. Penrose diagrams adapted to spacetimes with negative cosmological constant have been used in analyses by Jacob Bekenstein, John Preskill, Don Page, and Ted Jacobson to examine information flow and horizon structure in asymptotically AdS solutions such as the Schwarzschild–AdS metric and Reissner–Nordström–AdS metric studied by Roy Kerr and Hermann Reissner.
Anti-de Sitter serves as the vacuum background for a variety of exact solutions in general relativity including the Schwarzschild–AdS metric, Kerr–AdS metric, Reissner–Nordström–AdS metric, and lower-dimensional examples like the BTZ black hole. Analyses of stability, perturbations, and gravitational collapse in this background involve researchers such as Andrei B. Belinskii, V.A. Belinskii, Lev Landau, Evgeny Lifshitz, Miguel Alcubierre, and Piotr Chrusciel. The spacetime is also central to studies of positive energy theorems and conserved charges by Ed Witten, Stephen Hawking, Gary Gibbons, and Arnowitt Deser Misner.
The conjectured correspondence equates quantum gravity on an asymptotically AdS spacetime with a conformal field theory on its boundary, a duality proposed by Juan Maldacena and developed by Edward Witten, Steven Gubser, Igor Klebanov, Alexander Polyakov, Leonard Susskind, and Gerard 't Hooft. Key examples include the duality between type IIB string theory on AdS5×S5 and N=4 supersymmetric Yang–Mills theory analyzed by Michael Green, John Schwarz, Cumrun Vafa, and Nathan Seiberg. Holographic renormalization and correlation function computations were formalized by Kostas Skenderis, Vladimir Balasubramanian, Per Kraus, and M. Henningson.
Applications span computations of entanglement entropy via the Ryu–Takayanagi formula developed by Shinsei Ryu and Tadashi Takayanagi, studies of non-equilibrium dynamics by Shamit Kachru, Andrei Starinets, Hong Liu, and Dam Thanh Son, and condensed matter analogues investigated by Subir Sachdev, Sean Hartnoll, C.P. Herzog, and S. A. Hartnoll. The spacetime underpins model building in brane world scenarios by Lisa Randall, Raman Sundrum, and in explorations of quantum information aspects by Patrick Hayden, John Preskill, Fernando Pastawski, and Daniel Harlow. Experimental and observational implications are indirect but inform work by Planck Collaboration, LIGO Scientific Collaboration, Virgo Collaboration, and Event Horizon Telescope teams through theoretical constraints on cosmological models including those by Alan Guth and Andrei Linde.
Category:Spacetimes in general relativity