Models in Canonical General Relativity |
Metric Formulation, Reduced Models > s.a. models
in canonical quantum gravity [midisuperspaces and minisuperspaces].
@ One Killing vector field: Varadarajan PRD(95)gq [gauge fixing];
Balasin & Aichelburg GRG(07)-a0705 [pp-waves].
@ Spherical symmetry: Lund PRD(73);
Benguria et al NPB(77) [with Yang-Mills fields];
Gegenberg & Kunstatter PRD(12)-a1112 [collapse];
Shestakova a1303-MG13,
G&C(14) [in extended phase space];
Bodendorfer et al PRD(15)-a1506 [radial gauge];
> s.a. spherical symmetry.
@ Cylindrically symmetry: Mena PRD(01)gq/00 [gauge fixing];
Kouletsis et al PRD(03)gq;
> s.a. canonical formulation.
@ Locally homogeneous: Kodama PTP(98)gq/97;
Tanimoto et al JMP(97)gq,
gq/97-MG8.
> Models:
see bianchi models; FLRW models;
schwarzschild solution; spherical symmetry.
Metric Formulation, with Matter
> s.a. 2D gravity; 3D general relativity;
dirac fields; hamilton-jacobi theory;
perfect fluids.
@ Scalar field: Darian CQG(98)gq/97 [+ Maxwell, solving Hamiltonian];
Husain & Winkler PRD(05)gq [asymptotically flat, spherical];
> s.a. FLRW models.
@ Einstein-Maxwell theory: Arnowitt et al PR(60) [and point charge self-energy].
@ Thin shells: Hájíček PRD(98)gq [super-Hamiltonian],
JMP(99)gq/98 [+ black hole];
Hájíček & Kijowski PRD(00) [and time];
Hájíček & Kiefer NPB(01)ht/00 [embedding variables];
Hájíček & Kouletsis CQG(02)gq/01,
CQG(02)gq/01,
CQG(02)gq/01 [two shells];
Crisóstomo & Olea PRD(04)ht/03 [collapse];
Gladush GRG(04)gq/03;
Kijowski & Czuchry PRD(05)gq [non-spherical];
Fiamberti & Menotti NPB(08)-a0708 [intersecting];
Kijowski et al RPMP(09);
> s.a. gravitating matter
fields; metric matching.
@ Null shells: Louko et al PRD(98)gq/97;
Jezierski et al PRD(02)gq/01;
> s.a. spherical symmetry.
@ Other models: Nelson & Teitelboim PLB(77) [Einstein-Dirac];
Bičák & Kuchař PRD(97)gq [dust];
Kijowski & Magli CQG(98)gq/97 [thermoelastic, unconstrained];
Hájíček & Kijowski PRD(98)gq/97 [discontinuous fluid];
Steinhoff AdP(11)-a1106-PhD [spinning objects];
Date a1110 [fermions];
Schäfer & Jaranowski LRR(18)-a1805 [compact binaries, post-Newtonian dynamics];
> s.a. unimodular relativity [3-form].
Connection Formulation
> s.a. asympotic flatness at spatial infinity; bianchi
models; gowdy spacetime; instantons.
@ Spherical symmetry:
Bengtsson CQG(88);
Bombelli & Torrence CQG(90) [Kantowski-Sachs];
Fukuyama & Kamimura MPLA(91) [Schwarzschild];
Kamimura et al MPLA(91) [Schwarzschild-de Sitter];
Chakraborty2 NCB(00);
Ben Achour et al PRD(17)-a1608 [self-dual, with matter].
@ Bianchi models: Kodama PTP(88);
Schön pr(91) [I];
Calzetta & Thibeault gq/97/CQG [I, II, IX].
@ Geroch group: Mizoguchi PRD(95)gq/94.
@ Two-Killing vector field symmetry reductions: Husain PRD(96)gq;
Ashtekar & Husain IJMPD(98)gq/97 [Gowdy + cylindrical waves];
Zagermann CQG(98)gq/97.
@ Other symmetry reductions: Brodbeck & Zagermann CQG(00)gq/99 [higher-dimensional].
Connection Formulation, with Matter > s.a. connection
formulation of quantum gravity [fermions]; supergravity.
@ General references: Ashtekar et al PRD(89) [Klein-Gordon, Dirac, Yang-Mills];
Burnett et al pr(90);
Tsuda et al gq/95,
CQG(95)gq;
Tsuda & Shirafuji gq/96 [spin-3/2].
@ Scalar field: Capovilla PRD(92)gq [non-minimal];
Koshti CQG(92);
Montesinos et al JMP(99)gq,
Bojowald & Kagan PRD(06) [non-minimal];
Cianfrani & Montani PRD(09)-a0904 [non-minimal, without time gauge].
@ Barbero-Immirzi parameter as local field:
Taveras & Yunes PRD(08)-a0807;
Calcagni & Mercuri PRD(09)-a0902;
Mercuri & Taveras PRD(09)-a0903 [matter coupling and cosmology];
Torres-Gomez & Krasnov PRD(09) [with fermions];
Gates et al PRD(09)-a0906 [and 4D, N = 1 supergravity];
Cianfrani & Montani PRD(09);
Bombacigno et al PRD(16)-a1607 [cosmology, bounce];
> s.a. Peccei-Quinn Mechanism.
@ Fermion fields: Jacobson CQG(88);
Randono ht/05 [parity violation and Immirzi parameter];
Mercuri PRD(06)gq,
gq/06-MG9,
NCB(07),
PRD(08) [arbitrary γ];
Bojowald & Das PRD(08)-a0710 [real Ashtekar-Barbero variables];
Alexandrov CQG(08)-a0802 [role of the Immirzi parameter];
Kaźmierczak PRD(09)-a0812;
Cianfrani & Montani PRD(10)-a1001 [massless, non-minimal coupling].
@ Perfect fluids: Bombelli & Torrence CQG(90) [and Kantowski-Sachs models].
@ Maxwell field: Husain CQG(93)gq [Wilson loop variables].
@ Yang-Mills fields:
Chakraborty & Peldán IJMPD(94),
PRL(94).
Degenerate Metrics > s.a. extensions
of general relativity; types of metrics.
@ General references: Bengtsson IJMPA(89),
CQG(90),
GRG(93);
Maluf CQG(93);
Romano PRD(93)gq;
Reisenberger NPB(95)gq [diffeomorphisms and constraints];
Matschull CQG(96)gq/95;
Jacobson CQG(96)gq;
Lewandowski & Wisniewski CQG(97)gq/96,
CQG(99)gq;
Bengtsson & Jacobson CQG(97)gq;
Ma et al CQG(99)gq;
Ma & Liang GRG(98),
MPLA(98),
PRD(99)gq.
@ Solutions: Baez CMP(98)gq/97;
Yoneda et al PRD(97)gq [trick].
@ No-go results: in Bombelli & Torrence CQG(90).
main page
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