Anti-de Sitter Spacetime| 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 PRL(15)-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 PRD(19)-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];
Altas & Tekin PRD(19)-a1811 [new formulation];
Aneesh et al CQG(19)-a1902;
> 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 CQG(16)-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.
main page
– abbreviations
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– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 21 aug 2020