Anti-de Sitter Spacetime  

In General > s.a. Penrose Limit; quantum field theory in curved backgrounds; soliton; twistors.
$ Def: A spatially open, constant curvature cosmological solution of the Einstein equation with < 0.
* Topology: S1 × R3, with ctc's; The universal covering space (usually considered) is R4.
* Properties: There are no Cauchy surfaces; It is conformal to half the Einstein cylinder.
@ General references: in Hawking & Ellis 73.
@ Stability: Abbott & Deser NPB(82) [and canonical formalism]; Hawking CQG(00) [black holes and phase transitions]; Nayeri & Tran ht/04.
@ Related metrics: Bengtsson & Sandin CQG(06)gq/05 [2+1, squashed and stretched].
@ Quantum cosmology: Oliveira-Neto PRD(98) [Hartle-Hawking wave function, and cosmological constant quantization]; Bentivegna & Pawlowski a0803 [lqc].

Fields and Perturbations > s.a. AdS-cft; monopoles.
* Issue: AdS spacetime fails to be globally hyperbolic, so one needs to check to what extent field propagation in it is consistent and unambiguous.
@ Classical felds: Metsaev PLB(02) [massless fields in AdS5]; Ishibashi & Wald CQG(04)ht [general formulation]; Henneaux et al AP(07)ht/06 [with scalar, Hamiltonian and asymptotics]; > s.a. fields of arbitrary spin, klein-gordon.
@ Quantum felds: Deser & Levin CQG(97), Jacobson CQG(98)gq/97 [accelerated detectors]; > s.a. quantum field theory in curved backgrounds.

Asymptotically AdS Spacetimes > s.a. black hole solutions and thermodynamics; de sitter; kerr; schwarzschild; wormholes.
* Idea: They can be defined by a conformal completion method similar to the asymptotically flat case; The difference is that is timelike (it has topology R1 × S2), and the charges are absolutely conserved in the absence of matter – no news; The asymptotic symmetry group at spatial infinity is O(3, 2).
@ Conserved quantities: Ashtekar & Magnon CQG(84); Davis PLB(86); Henneaux & Teitelboim CMP(85); Henneaux in(86); Pinto & Soares PRD(95); Ashtekar & Das CQG(00)ht/99; Pinto-Neto & Rodrigues PRD(00)gq; Chrusciel & Nagy CQG(01)ht/00, ATMP(01)gq [mass]; Galloway et al CMP(03) [geometry and mass, soliton]; Barnich et al gq/03-in; Okuyama & Koga PRD(05)ht [higher-curvature and d 4]; Hollands et al CQG(05)ht [comparison between definitions]; Chrusciel et al JHEP(06)gq [upper bounds on angular momentum and center of mass]; > s.a. charge.
@ Locally asymptotically AdS spacetimes: Aros et al PRL(00)gq/99, PRD(00)gq/99 [charges]; Anderson CQG(06)ht [uniqueness].
@ Cosmological solutions: Hertog & Horowitz JHEP(05)ht [sugra, singular, holographic].
@ In 3D: Carlip CQG(05)gq [asymptotic diffeomorphisms as dynamical degrees of freedom]; > s.a. 3D general relativity and gravity; 3D black holes [including BTZ].
@ In > 4D: Clarkson & Mann PRL(06) [asymptotically AdS5/, but less energy]; Giovannini CQG(06) [5D].
> Related topics: see action; causality violations; gravitational collapse; gravitational energy and positivity; killing tensors [Killing-Yano].

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