Anti-de Sitter Spacetime  

In General > s.a. geodesics; Penrose Limit; solitons; twistors.
$ Def: A spatially open, constant curvature cosmological solution of the Einstein equation with Λ < 0.
* Topology: S1 × \(\mathbb R\)3, with closed timelike curves; The universal covering space (usually considered) is \(\mathbb R\)4.
* Properties: There are no Cauchy surfaces; It is conformal to half the Einstein cylinder.
@ General references: in Hawking & Ellis 73; Barbot et al a1205 [open questions]; Sokołowski IJGMP(16)-a1611 [geometry]; > s.a. coordinates.
@ Related metrics: Bengtsson & Sandin CQG(06)gq/05 [2+1, squashed and stretched]; Magueijo & Mozaffari CQG(10)-a0911 [generalized].
@ Quantum cosmology: Oliveira-Neto PRD(98) [Hartle-Hawking wave function, and cosmological constant quantization]; Bentivegna & Pawłowski PRD(08)-a0803 [lqc].
> Online resources: see Wikipedia page.

Fields and Perturbations > s.a. AdS-cft correspondence; monopoles; Tensor Networks [AdS/MERA correspondence].
* Issue: AdS spacetime fails to be globally hyperbolic, so one needs to check to what extent field propagation in it is consistent and unambiguous.
* Stability: 2015, The issue of the stability of the Einstein-scalar-field equations with negative cosmological constant is not settled.
@ Classical fields: 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 fields.
@ Stability: Abbott & Deser NPB(82) [and canonical formalism]; Hawking CQG(00) [black holes and phase transitions]; Nayeri & Tran ht/04; Faulkner et al CQG(10)-a1006 [with scalar field]; Bizoń & Rostworowski PRL(11)-a1104 [generic instability triggered by turbulence]; Dias et al CQG(12)-a1208 [non-linear stability]; Friedrich CQG(14)-a1401; Horowitz & Santos a1408-in [and geons]; Maliborski & Rostworowski PRL(13)-a1303 [non-linear stability around time-periodic solutions], IJMPA(13)-a1308, PRD(14)-a1403 [what drives the instability]; Bizoń GRG(14)-a1312-GR20 [weak turbulence as a driving mechanism]; Deppe et al PRL(15)-a1410 [in Einstein-Gauss-Bonnet gravity]; Balasubramanian et al PRL(14)-a1403, comment Bizoń & Rostworowski a1410, reply Buchel et al PRL(15)-a1506 [non-unstable and quasiperiodic solutions]; Bizoń et al PRL(15)-a1506 [resonant system with oscillatory singularity in finite time]; Gürsoy et al PRD(16)-a1603 [Einstein-scalar, dynamical instability]; Deppe a1606.
@ Higher-dimensional: Metsaev PLB(02) [massless fields in AdS5]; Bachelot JMPA(11)-a1010 [massive fields in AdS5].
@ Particle detectors: Deser & Levin CQG(97); Jacobson CQG(98)gq/97; Jennings CQG(10)-a1008.
> Quantum fields: see quantum field theory in curved backgrounds.

Asymptotically AdS Spacetimes > s.a. black-hole solutions and thermodynamics; kerr solutions; schwarzschild spacetime; wormholes.
* Idea: They can be defined by a conformal completion method similar to the asymptotically flat case; The difference is that \(\cal I\) is timelike (it has topology \(\mathbb R\)1 × 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).
@ General references: Kelly & Marolf CQG(12)-a1202 [two types of phase space formulations]; Hubeny et al JHEP(13)-a1306 [causal wedges].
@ 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; Chruściel & Nagy CQG(01)ht/00, ATMP(01)gq [mass]; Galloway et al CMP(03) [geometry and mass, soliton]; Barnich et al NPPS(04)gq/03; Okuyama & Koga PRD(05)ht [higher-curvature and d ≥ 4]; Hollands et al CQG(05)ht [comparison between definitions]; Chruściel et al JHEP(06)gq [upper bounds on angular momentum and center of mass]; Fischetti et al a1211-ch [rev]; Wen a1503 [mass, Hamiltonian and Wald formula, with matter couplings]; > 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 [supergravity, singular, holographic]; > s.a. de sitter space.
@ In 3D: Carlip CQG(05)gq [asymptotic diffeomorphisms as dynamical degrees of freedom]; Henneaux et al PRD(10)-a1006 [in topologically massive gravity]; Bombelli & Mohd a1111-MG12 [global charges, trace anomaly]; > s.a. 3D general relativity and gravity; 3D black holes [including BTZ].
@ Propagating fields: Warnick CMP(13)-a1202 [massive wave equation].
@ In quantum gravity: Bodendorfer a1512 [lqg].
@ In higher dimensions: Clarkson & Mann PRL(06) [asymptotically AdS5/Γ, but less energy]; Giovannini CQG(06) [5D].
> Related topics: see action; causality violations; gravitational collapse; gravitational energy and positivity; killing tensors [Killing-Yano]; modified general relativity [anti-de Sitter tangent group]; Topologically Massive Gravity.


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