Formalism
Definition
Spacetime configurations
Properties
Spacetimes
black hole spacetimes | vanishing angular momentum | positive angular momentum |
---|---|---|
vanishing charge | Schwarzschild spacetime | Kerr spacetime |
positive charge | Reissner-Nordstrom spacetime | Kerr-Newman spacetime |
Quantum theory
Up to isometry, the anti de Sitter spacetime of dimension , , is the pseudo-Riemannian manifold whose underlying manifold is the submanifold of the Minkowski spacetime that solves the equation
for some (the “radius” of the spacetime) and equipped with the metric induced from the ambient metric, where denote the canonical coordinates. is homeomorphic to , and its isometry group is .
More generally, one may define the anti de Sitter space of signature as isometrically embedded in the space with coordinates as the sphere .
(…)
in horospheric coordinates the AdS metric tensor is
In terms of
this becomes
and with
for
we get
(…)
Asymptotically anti-de Sitter spaces play a central role in the realization of the holographic principle by AdS/CFT correspondence.
Matthias Blau, chapter 38 of Lecture notes on general relativity (web)
Ingemar Bengtsson, Anti-de Sitter space, lecture notes (pdf)
Leonardo Castellani, Riccardo D'Auria, Pietro Fré, volume 1, chapter I.3.8 of Supergravity and Superstrings - A Geometric Perspective, World Scientific (1991)
C. Frances, The conformal boundary of anti-de Sitter space-times, in AdS/CFT correspondence: Einstein metrics and their conformal boundaries , 205–216, IRMA Lect. Math. Theor. Phys., 8, Eur. Math. Soc., Zürich, 2005 (pdf)
Gary Gibbons, Anti-de-Sitter spacetime and its uses (arXiv:1110.1206)
Makoto Natsuume, section 6 of AdS/CFT Duality User Guide, Lecture Notes in Physics 903, Springer 2015 (arXiv:1409.3575)
Wikipedia (English): anti de Sitter space
Abdelghani Zeghib, On closed anti de Sitter spacetimes, Math. Ann. 310, 695–716 (1998) (pdf)
Leszek M. Sokolowski, The bizarre anti-de Sitter spacetime, International Journal of Geometric Methods in Modern Physics 13 no.9 (2016) 1630016 (arXiv:1611.01118)
Discussion of thermal Wick rotation on global anti-de Sitter spacetime (which is already periodic in real time) to Euclidean field theory with periodic imaginary time is in
Discussion of black holes in anti de Sitter spacetime:
Hawking, Stephen W., and Don N. Page. “Thermodynamics of black holes in anti-de Sitter space.” Communications in Mathematical Physics 87.4 (1983): 577-588.
M. Socolovsky, Schwarzschild Black Hole in Anti-De Sitter Space (arXiv:1711.02744)
Peng Zhao, Black Holes in Anti-de Sitter Spacetime (pdf)
Jakob Gath, The role of black holes in the AdS/CFT correspondence (pdf)
Revision on November 15, 2018 at 15:41:37 by Urs Schreiber See the history of this page for a list of all contributions to it.