3-Dimensional Classical Gravity Theories  

In General > s.a. 3D general relativity; 3D quantum gravity; Scalar Theory.
* Massive gravity: Theories obtained by adding to Einstein's gravity the usual Fierz-Pauli, or the more complicated Ricci scalar squared (R2), terms, are tree level unitary, but have their unitarity spoiled when a Chern–Simons term is added (topologically massive).
@ Quadratic: Accioly et al JPA(01) [with Chern-Simons term], PLA(01), MPLA(01), PRD(03) [with Chern-Simons term]; Accioly & Dias MPLA(04) [unitarity]; > s.a. higher-order gravity.
@ Deformed: Mignemi IJMPA(05)ht/04 [deformed anti-de Sitter algebra, solutions]
@ Non-commutative: Valtancoli CQG(05)ht [with pointlike sources]; Schroers PoS-a0711 [lessons learned].
@ Black holes: Yamazaki & Ida PRD(01) [Einstein-BI-dilaton]; Sousa & Maluf PTP(02)gq/03 [teleparallel]; > s.a. 3D black holes.
@ With topological matter: Gegenberg et al PLB(90); Mann & Popescu CQG(06)gq/05 [0-form and 2-form].
@ Supersymmetric: Guadagnini et al PLB(90); Cvetkovic & Blagojevic CQG(07)gq [with torsion].
@ Other theories: Cornish & Frankel PRD(91); Waelbroeck NPB(91) [time]; Zanelli ht/00-ln [Chern-Simons gravity]; Bezerra et al gq/01 [Jackiw's]; Fernando GRG(02)gq [rotating dilaton solutions]; Cacciatori et al PLB(02)gq [Einstein-AdS]; Alonso et al PRD(03) [Brans-Dicke]; Blagojevic & Cvetkovic in(06)gq/04 [with torsion]; Mann & Popescu IJMPA(07)gq/06 [and higher-rank gauge theory]; Arias & Gaitan FPC(09)-a0709 [self-dual spin-2 theory]; Bergshoeff et al PRL(09)-a0901 [higher-order theory, and massive Pauli-Fierz].
@ Related topics: Hellerman a0902 [with negative cosmological constant, maximum mass of excitation]; > s.a. bimetric gravity.
> Phenomenology: see gravitational collapse.

Chern-Simons Form, Topological Gravity > s.a. 3D general relativity; black holes in modified theories; Metric-Affine; Topological Gravity.
* For vanishing cosmological constant: 3D general relativity, formulated as an ISO(2,1)-Chern-Simons gauge theory, which is integrable; If the phase space is chosen to be that of flat connections modulo gauge transformations, the theory is purely topological.
* For non-vanishing cosmological constant: For positive , general relativity can be formulated as a SO(3,1) gauge theory, and for negative , as a SO(2,2) gauge theory.
@ General references: Achúcarro & Townsend PLB(86); Rocek & Van Nieuwenhuizen CQG(86); Teitelboim & Zanelli CQG(87); Holz CQG(88); Witten PLB(88); Bengtsson PRD(89); Myers NPB(90), PLB(90); Myers & Periwal NPB(90); Soda & Yamanaka MPLA(91); Birmingham & Rakowski GRG(93); Aliev & Nutku CQG(95)gq/98, CQG(96)gq/98; Meusburger & Schroers CQG(03)ht; Deser & Tekin CQG(03)gq [energy]; Park JHEP(08)-a0805 [degrees of freedom and gravitons].
@ Lattice version: Waelbroeck CQG(90).
@ Quantization: Percacci AP(87).

Topologically Massive Gravity
* Action: The Einstein action ( ISO(2,1) Chern-Simons) plus a conformal gravity term ( SO(2,1)-Chern-Simons or SO(3)-Chern-Simons).
* Field equations: If m is the topological coupling constant, and C the (traceless) Cotton tensor, then

Gab + m–1 Cab = –k Tab .

@ General references: Peldán CQG(92); Deser et al NPB(94)ht/93 [particle scattering amplitudes]; Grumiller & Jackiw a0802-wd [with < 0, and complex Chern-Simons terms]; Hotta et al JHEP(08)-a0805 [canonical approach]; Carlip JHEP(08)-a0807 [AdS, constraint algebra]; Grumiller et al a0806 [cosmological, at the chiral point]; Blagojevic & Cvetkovic JHEP(09)-a0812 [canonical structure]; > s.a. 3D quantum gravity.
@ Solutions: Nutku & Baekler AP(89); Clément CQG(90); Ortiz AP(90), CQG(90); Edery & Paranjape PLB(97), PLB(97)gq; Dereli & Sarioglu gq/00 [black holes], PLB(00)gq [+ Maxwell-Chern-Simons, self-dual]; Accioly & Dias IJMPA(06)ht/05 [non-unitarity].

Conformal Gravity > s.a. [Conformal Gravity]; topological field theory.
* Action: In Chern-Simons form for connection defined in terms of dreibein; SO(3,2) gauge theory.
@ General references: Deser et al AP(82), PRL(82); Horne & Witten PRL(89); Mannheim in(91); Vaz & Witten NPB(92).
@ Related topics: García-Compeán et al PRD(00)ht/99 [self-dual].

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