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| AdS-Schwarzschild | |
|---|---|
| Name | AdS-Schwarzschild |
| Field | Theoretical physics |
| Associated people | Hermann Schwarz, Albert Einstein, David Hilbert, Juan Maldacena, Stephen Hawking, Roger Penrose, Subrahmanyan Chandrasekhar, Jacob Bekenstein, Gerard 't Hooft, Leonard Susskind, Kip Thorne, James Hartle, Gary Gibbons, Rob Myers, Edward Witten, Andrew Strominger, Juan Maldacena |
| Year discovered | 1963 |
AdS-Schwarzschild is a family of exact solutions of the Einstein field equations that describe non-rotating, uncharged black holes in a spacetime with negative cosmological constant, linking Albert Einstein's relativistic gravity, Hermann Schwarz's metric work, and modern developments in string theory and quantum gravity. The solution underpins analyses in the AdS/CFT correspondence, thermodynamic behavior studied by Stephen Hawking and Jacob Bekenstein, and perturbative stability researched by groups around Roger Penrose and Gary Gibbons. It plays a central role in comparing semiclassical Gerard 't Hooft and holographic descriptions proposed by Leonard Susskind and Edward Witten.
The AdS-Schwarzschild spacetime extends the classical Schwarzschild metric into asymptotically anti-de Sitter space first considered in contexts influenced by Albert Einstein's cosmological constant and later applied in string theory by work of Juan Maldacena, Edward Witten, Hugh Osborn, Gary Gibbons, and Roman Jackiw. It is characterized by a mass parameter linked to the ADM energy defined in the formalism of Arnowitt–Deser–Misner and features an event horizon whose radius depends on the mass and the AdS length scale often denoted by parameters introduced by Max Planck and operationalized in semiclassical analyses by Stephen Hawking and James Hartle. Globally, the solution shares causal structures with the Schwarzschild geometry while exhibiting reflecting boundary conditions at spatial infinity used in work by Paul Dirac, Julian Schwinger, Kip Thorne, and Subrahmanyan Chandrasekhar.
The metric is usually presented in static coordinates analogous to the original Schwarzschild coordinates employed by Hermann Schwarz and adapted to negative curvature as in anti-de Sitter space studies by Maximilian Kretschmann and later coordinate charts developed by Roger Penrose and Stephen Hawking. Alternative charts include Eddington–Finkelstein coordinates introduced by Arthur Eddington and David Finkelstein, Kruskal–Szekeres coordinates owing to Martin Kruskal and George Szekeres, and Fefferman–Graham expansions associated with Charles Fefferman and Robin Graham used extensively in holographic renormalization by Edward Witten and Kostas Skenderis. These coordinate systems facilitate analyses of causal structure explored by Roger Penrose and conformal boundary behavior exploited by Juan Maldacena, Leonard Susskind, Gerard 't Hooft, and Andrei Sakharov.
AdS-Schwarzschild black holes display thermodynamic behavior first described in Hawking–Page phase transitions introduced by Stephen Hawking and Don Page, forming a canonical example linking semiclassical entropy from Jacob Bekenstein to quantum field theory ensembles treated by Richard Feynman, Julian Schwinger, and Syukuro Manabe. The Hawking temperature, Bekenstein–Hawking entropy, and free energy interplay underlies phase structure analogous to transitions studied by Lev Landau and Isaac Newton in thermodynamics, and is central to the holographic confinement/deconfinement correspondence analyzed by Edward Witten, David Gross, Frank Wilczek, and David Politzer. Large versus small black hole phases relate to stability analyses pursued by Gary Gibbons and Rob Myers, and to dual phenomena in conformal field theory studied in the framework advanced by Alexander Polyakov and Kenneth Wilson.
Linear and nonlinear stability of AdS-Schwarzschild spacetimes has been probed using techniques from perturbation theory developed by Subrahmanyan Chandrasekhar, Teukolsky, and Vishveshwara and by modal analyses championed by Katherine Freese and Vladimir Belinski. Quasinormal mode spectra first computed in relativistic perturbation studies by Regge and Wheeler inform decay rates and echo phenomena related to work by Clifford Will and observational implications tied to Kip Thorne and B. P. Abbott's collaborations. Nonlinear instability and turbulent cascades in AdS contexts have been investigated by groups including Mihalis Dafermos, Giorgio Parisi, and Ofer Aharony, leveraging numerical relativity methods developed by Frans Pretorius and Matthew Choptuik.
AdS-Schwarzschild is a prototypical bulk geometry in the AdS/CFT correspondence proposed by Juan Maldacena and formalized by Edward Witten and Steven Gubser, providing dual descriptions to thermal states in N=4 supersymmetric Yang–Mills theory and related conformal field theory models studied by Alexander Polyakov, Kenneth Wilson, and Gerard 't Hooft. It underlies holographic calculations of transport coefficients pioneered by Dam Thanh Son and Andrei Starinets, entanglement entropy formulas linked to Ryu–Takayanagi and extensions by Tadashi Takayanagi, and thermalization scenarios examined by Paul Chesler and Larry Yaffe. Applications span connections to condensed matter models studied by Subir Sachdev and Patrick Lee and to quark–gluon plasma phenomenology investigated by Edward Shuryak and Dirk H. Rischke.
Generalizations include charged Reissner–Nordström–AdS solutions connected to Karl Schwarzschild and Georges Lemaître's work, rotating Kerr–AdS metrics extending Roy Kerr's solution, higher-dimensional black holes studied in Tangherlini and in supergravity contexts by Michael Duff and Chris Hull, and hairy black holes explored in scalar condensation studies involving Steven Weinberg and John Preskill. Further extensions appear in Lovelock gravity investigated by David Lovelock, Gauss–Bonnet corrections examined by David G. Boulware and Sean Carroll, and in string theoretic embeddings constructed by Joseph Polchinski and Andrew Strominger. These generalizations inform ongoing research by institutions including Institute for Advanced Study, Perimeter Institute, CERN, Princeton University, Harvard University, and Caltech.