2-Dimensional Classical Gravity  

In General > s.a. 2D manifolds; 2D quantum gravity / 2D black holes; black-hole entropy [corrections]; entropy bounds; geons [kinks].
* Remark: Any metric solves the vacuum Einstein equation, so to get something interesting one has to modify the theory slightly; General matterless models of gravity include theries a dilaton, arbitrary powers in curvature, or dynamical torsion; They are a special class of "Poisson-sigma-models" whose solutions are known completely, together with their general global structure; Besides the ordinary black hole, arbitrary singularity structures can be studied.
* Solvability: All 2D models of gravity – including theories with non-vanishing torsion and dilaton theories – can be solved exactly if matter interactions are absent; An absolutely conserved quantity determines the global classification of all solutions; In the case of spherically reduced general relativity it coincides with the mass in the Schwarzschild solution.
@ Overview: in Brown 88; Gegenberg et al PRD(88); Mohammedi pr(90); Kummer gq/96; Strobl Hab(99)ht/00.
@ Canonical form: Kummer & Lau AP(97)gq/96 [boundary conditions, quasilocal energy]; Constantinidis et al PRD(00)ht/99 [gauge fixing and reduced phase space]; Kiriushcheva et al MPLA(05)ht, MPLA(05)ht, Kiriushcheva & Kuzmin MPLA(06), AP(06)ht/05 [canonical form of Einstein-Hilbert action]; Gambini et al CQG(10)-a0909, comment Bojowald et al a1706 [Ashtekar-type variables]; Gegenberg & Kunstatter a1504 [as modified Yang-Mills theory]; McKeon a1607 [Palatini action, symplectic analysis].
@ Einstein-Hilbert theory: da Rocha & Rodrigues MPLA(06)ht/05, comment Kiriushcheva & Kuzmin ht/06 [Lagrangian]; de Lacroix & Erbin a1612 [with non-conformal matter, degrees of freedom].
@ AdS-cft, boundary field theory: Cadoni et al PRD(01)ht/00; Cadoni & Carta MPLA(01)ht/01-in [dilaton].
@ Solutions: Cooperstock & Faraoni GRG(95) [gravitational radiation]; Klösch & Strobl gq/97-MG8 [classification].
@ And matter: Ohta & Mann CQG(96)gq [with point particles, canonical reduction]; Ambjørn et al MPLA(97) [Ising matter]; Mann CQG(01) [N particles, on S1]; Boozer PRD(10) [point particles].
@ Related topics: Deser FP(96)gq/95 [inequivalence of Palatini and metric forms]; Kummer & Tieber PRD(99)ht/98 [symmetries and conservation laws]; Boozer EJP(08) [toy model]; Bertin et al AP(10)-a0911 [general relativity, Hamilton-Jacobi constraint analysis].

Dilaton Theories > s.a. dilaton; black holes; cosmic censorship; semiclassical general relativity [limits of validity].
* Remark: One version can be obtained from the spherical reduction of 4D general relativity.
@ General references: Klösch et al HPA(96)gq; Klösch NPPS(97)gq; Grumiller et al AP(01)gq/00 [2 dilatons]; Alves & Bezerra IJMPD(00)gq [+ scalar]; Cavaglià AIP(98)ht, PRD(99)ht/98, Grumiller et al MPLA(01)gq/00 [matterless], PRP(02) [rev, especially black holes]; Mignemi PLB(03)ht/02 [with torsion].
@ With particles: Rivelles NPPS(00)ht/99.
@ Related topics: Hayward CQG(93)gq/92 [censorship]; Cruz & Navarro-Salas MPLA(97) [free field theory equivalence]; Grumiller et al UJP(03)ht-in [triviality of κ-deformations]; Grumiller & Jackiw PLB(06) [duality].

Jackiw-Teitelboim Theory > s.a. 2D quantum gravity; 3D gravity [extension]; black holes.
* Field equations: Simply R = T.
@ General references: Teitelboim PLB(83), in(84); Jackiw in(84), NPB(85); Henneaux PRL(85); Torre PRD(89); Sikkema & Mann CQG(91); Moayedi & Darabi JMP(01)gq/00 [with electromagnetism]; Brigante et al JHEP(02)ht [with cosmological constant]; Cadoni & Mignemi GRG(02)gq [cosmology]; Constantinidis et al CQG(08)-a0802 [canonical analysis]; Alkalaev JPA(14) [higher-spin extension].
@ Other solutions: Mann & Ohta CQG(00)gq/01 [2-body]; Reyes JPA(06) [solitons].

Other Theories > s.a. emergent gravity [entropic]; Liouville Theory; Matrix Models; supergravity; topological field theories.
@ Topological gravity: Rajeev PLB(82) [quantum, solution]; Li PRD(86), NPB(90) [W-gravity]; Labastida & Pernici PLB(88) [Lagrangian]; Labastida et al NPB(88); Chamseddine & Wyler PLB(89), NPB(90); Witten NPB(90).
@ Topological gravity with matter: Killingback PLB(91), PLB(91).
@ Higher-derivative: Schmidt JMP(91); Schmidt GRG(99) [and Einstein-dilaton]; Ahmed a1112 [f(R) theories]; > s.a. black holes.
@ Quadratic with torsion: Grosse et al JMP(92)ht; Katanaev et al PRD(96)gq/95 [relation to dilaton]; Mignemi AP(97)gq/95 [Riemann-Cartan].
@ Supergravity: Ertl et al NPB(98)ht/97.
@ Discrete, Lorentzian triangulations: Di Francesco et al NPB(00) [and random walks], NPB(01)ht/00 [and Calogero Hamiltonian];
@ Non-commutative: Cacciatori et al CQG(02)ht; Balachandran et al CQG(06)ht [in terms of non-commutative gauge theories].
@ More theories: Schaller & Strobl ht/93 [with torsion]; Amelino-Camelia et al PRD(96)ht [string-inspired, and Yang-Mills theory]; Obukhov PRD(04)gq/03 [metric-affine]; Frolov et al GRG(10)-a0901 [algebraic analysis]; Klusoň PRD(12)-a1110 [massive gravity, Hamiltonian analysis].


main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 2 jul 2017