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]; > 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 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 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 pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 10 sep 2016