Non-Commutative Gravity
blue bullet Theories of gravity based on non-commutative geometry; see also non-commutative spacetime.

In General > s.a. 2D gravity; 3D gravity; general relativity action; gravity as a gauge theory [on a fuzzy space]; non-commutative cosmology.
* Idea: A number of particle theories, such as gauge theories or Connes' description of the standard model of elementary particles, use non-commutative spacetimes as models for quantum spacetime (with or without breaking of Lorentz symmetry), and approaches to quantum gravity such as loop gravity and string theory, also lead to effective non-commutative descriptions of spacetime.
* Motivation: This may provide a framework in which one can "smoothly" interpolate between spatial topologies; UV-divergences in quantum field theory.
* Einstein equation: The effects of non-commutativity can be taken into account by keeping the standard form of the Einstein tensor on the left-hand side of the equation and introducing a modified energy-momentum tensor as a source on the right-hand side.
* Remark: Alain Connes' non-commutative theory includes the standard model of particle physics and euclidean gravity.
* Remark: The Wodzicki residue of D−2, with D the Dirac operator, is proportional to the Einstein-Hilbert action [@ Kastler CMP(95)].
@ Reviews: Fröhlich et al ht/97-ln; Chamseddine AIHP(03)ht-conf; Meyer ht/05-conf; Yang MPLA(07)ht/06; Vassilevich a0902-ch; Franco a0904-proc; Martinetti JPCS(15)-a1510; Connes a1703-in.
@ General references: Gervais NPB(87); Chamseddine et al CMP(93); Landi et al PLB(94); Mohammedi MPLA(94); Sitarz CQG(94)ht; Connes CMP(96)ht [matter]; Madore NPPS(97)gq/96, gq/97; Bimonte et al NPB(98)ht/97, PLB(98)gq; Jevicki & Ramgoolam JHEP(99) [from AdS-cft]; Chamseddine PLB(01)ht/00 [gauged non-commutative ISO(3,1) group]; Nair NPB(03)ht/01; Cardella & Zanon CQG(03)ht/02 [deformation]; Rivelles PLB(03)ht/02; Chamseddine JMP(03) [action]; Avramidi PLB(03)ht [deformation]; Aschieri et al CQG(05)ht [metric, curvature, torsion, action], CQG(06)ht/05, Aschieri JPCS(06)ht [deformed diffeomorphisms]; Calmet & Kobakhidze PRD(05)ht [general relativity]; Kobakhidze IJMPA(08)ht/06; Dobrski PRD(11)-a1011 [Fedosov deformation]; Anagnostopoulos et al ed-GRG(11)#9; Schenkel PhD-a1210; Di Grezia et al PRD(14)-a1312 [from twist-deformed products in the general relativity action]; Nair PRD(15)-a1508 [using thermofield dynamics]; Dobrski CQG(17)-a1512; de Cesare et al CQG(18)-a1806 [with self-dual variables].
@ Corrections to the Einstein equation: Mukherjee & Saha PRD(06); Fucci & Avramidi CQG(08)-a0708 [and matter energy-momentum]; Much et al a1705.
@ Lorentzian version: Kobakhidze EJTP-a0905 [diffeomorphism-invariant version, with twisted local Lorentz invariance]; Franco AIP(10)-a1003.
@ Linearized gravity: Ferrari et al PLB(07)ht/06 [Lorentz violation and torsion]; > s.a. modified quantum gravity.
@ From string theory: Álvarez-Gaumé et al NPB(06); Freidel et al PRD(17)-a1707 [zero-mode sector of closed string theory].
@ From gauge theories: Yang EPL(09)ht/06, IJMPA(09)ht/06 [self-dual electromagnetism]; Steinacker JHEP(07)-a0708 [non-commutative U(n) gauge theory], CQG(10) [matrix models]; Cortese & García PRD(10)-a1001 [deformed gauge theory]; Manolakos et al a1907, JHEP(20)-a1902; > s.a. Matrix Models.
@ Related topics: Rivelles AIP(05)ht/04 [and Seiberg-Witten map]; Zupnik CQG(07) [reality]; Nguyen a1512 [and unification]; > s.a. Star Product.

Solutions, Matter and Related Aspects > s.a. gravitational radiation; non-commutative physics [including astrophysics and other phenomenology].
@ Schwarzschild black holes: López-Domínguez et al PRD(06)ht [and thermodynamics]; Chaichian et al PLB(08)-a0710, Kobakhidze PRD(09)-a0712 [corrections]; Banerjee & Gangopadhyay GRG(11)-a1008 [Komar energy and Smarr formula]; > s.a. schwarzschild solution.
@ BTZ black holes: Dolan et al CQG(07) [and discrete time]; Rahaman et al PRD(13)-a1301; Gupta et al AHEP(14)-a1312 [black-hole entropy].
@ Other black holes: Nozari & Fazlpour MPLA(07)ht/06 [evaporating]; Mukherjee & Saha PRD(08)-a0710 [corrections to Reissner-Nordström]; Chaichian et al JHEP(08) [including cosmological constant]; Nicolini IJMPA(09)-a0807 [rev]; Estrada-Jiménez et al PRD(08) [twisted, covariant, self-dual]; Schupp & Solodukhin a0906 [exact solutions]; Ohl & Schenkel JHEP(09)-a0906 [twisted]; Alavi APPB(09)-a0909 [Reissner-Nordström]; Bastos et al PRD(09) [thermodynamics]; Modesto & Nicolini PRD(10)-a1005 [charged rotating]; Mbonye a1007-GR19; Brown & Mann PLB(10)-a1012 [Reissner-Nordström black hole]; Mureika & Nicolini PRD(11)-a1104 [1+1]; Mann & Nicolini PRD(11)-a1102 [cosmological pair production]; Bastos et al AIP(12)-a1202 [non-canonical phase-space non-commutative black holes]; Gangopadhyay MPLA(13)-a1303 [and the Voros product]; Hassannejad a1911 [entropy]; > s.a. black holes in higher dimensions; black-hole radiation; finsler geometry; quantum black holes; Vaidya Metric.
@ Other solutions: Aschieri & Castellani JGP(10)-a0906; > s.a. Gravastars; models of topology change; wormholes.
@ And other fields: Brandt & Elias PRD(06)ht [scalar-graviton interaction]; Yang JHEP(09)-a0809 [and electromagnetism, emergent gravity]; Aschieri & Castellani JHEP(09)-a0902 [coupled to fermions], JHEP(09)-a0902 [3D and 4D supergravity]; Aastrup et a CQG(11)-a1012 [coupling to matter, and semiclassical approximation]; Aschieri & Castellani GRG(13)-a1205 [non-commutative gauge fields], GRG(13)-a1206 [scalar fields].
@ Large extra dimensions: Lizzi et al MPLA(01)ht/00 [Randall-Sundrum]; Nicolini & Winstanley JHEP(11)-a1108 [Hawking radiation].

Quantum Gravity > s.a. discrete models; non-commutative cosmology [quantum cosmology]; photons in quantum gravity.
@ General references: Moffat PLB(00)ht, PLB(00)ht [perturbative]; Vassilevich NPB(02) [2D, Moyal]; Heller et al IJTP(05)gq, GRG(04)gq/05, JMP(05); Martinetti MPLA(05)gq-in [and thermal time hypothesis]; Lee & Yang JKPS(14)-a1004; Gracia-Bondía in(10)-a1005-ln; Bianchi & Rovelli PRD(11)-a1105 [interpretation]; Faizal MPLA(13)-a1302 [perturbative, BRST and anti-BRST symmetries]; Kober IJMPA-a1409 [on non-commutative spacetime].
@ Introductions, reviews: Aastrup & Grimstrup IJMPA(07)ht/06; Chamseddine & Connes PRL(07) [boundary terms from spectral action], CMP(10)-a0812; Aastrup & Grimstrup Sigma(12)-a1203.
@ Spectral action: Iochum et al CMP(12)-a1008 [for torsion]; Chamseddine & Connes JGP(11)-a1008 [for manifolds with boundary]; Sakellariadou IJMPD(11) [rev]; Aastrup & Grimstrup CQG(14)-a1105 [and emergent fermionic quantum field theory]; Ćaćić et al JNCG(14)-a1106 [coupling to matter]; Sakellariadou a1204-conf, JPCS(13) [rev]; Devastato PLB(14)-a1309 [extension to the Planck scale]; Chamseddine et al PRL(14)-a1409 [quanta of geometry]; Sakellariadou & Watcharangkool PRD(16)-a1601 [linear stability]; Singh a1906-GR22; Maithresh & Singh a1908.
@ And lqg: Aastrup et al CQG(09)-a0802, JNCG(09)-a0802, CQG(09)-a0902-conf; Aastrup & Grimstrup CQG(13)-a1209, a1209 [holonomy-diffeomorphism algebra].
@ 3D: Schroers PoS-a0710 [phase-space non-commutativity], a1105-conf; > s.a. 3D quantum gravity.
@ And quantum mechanics: Heller et al JMP(00)ht/99; Singh et al gq/05 [non-linear].
@ Phenomenology: Heller & Sasin JMP(96), JMP(97)gq, GRG(99)gq/98 [and singularities]; Girelli & Livine gq/04, Girelli et al NPB(05)gq [low-energy limit]; Heller et al JMP(07) [malicious singularities]; > s.a. kaluza-klein phenomenology; pioneer anomaly; singularities.

"Non-commutative geometry does not purport yet to solve the riddle of quantum gravity; it is
more of an insurance policy against the probable failure of the other approaches." J M Gracia-Bondía

main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at – modified 16 aug 2020