Non-Commutative
Gravity| Non-Commutative
Gravity |
In General > s.a. 2D gravity; 3D
gravity; action
for general relativity.
* Motivation: May be
able to "smoothly" interpolate between
different spatial topologies.
* 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: 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-in;
Meyer ht/05-in;
Yang MPLA(07)ht/06;
Vassilevich a0902-in;
Franco a0904-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]; 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;
Harikumar & Rivelles CQG(06)ht [and
non-associative]; Mukherjee & Saha PRD(06)
[non-commutative corrections]; Fucci & Avramidi CQG(08)-a0708 [non-commutative
Einstein equation]; Kobakhidze a0905 [diffeomorphism-invariant
version, with twisted local Lorentz invariance]; Aschieri & Castellani a0906 [solutions].
@ Cosmological constant: Yang a0711 [from
fluctuations, emergent gravity]; Mena et al a0802.
@ Linearized gravity: Ferrari et al PLB(07)ht/06 [Lorentz
violation and torsion]; > s.a. modified quantum gravity.
@ 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].
@ From string theory: Álvarez-Gaumé et al NPB(06).
@ From other theories: Yang ht/06,
IJMPA(09)ht/06 [from
self-dual electromagnetism]; Steinacker JHEP(07)-a0708 [from
non-commutative U(n) gauge
theory].
@ Black holes: Nozari & Fazlpour MPLA(07)ht/06 [evaporating];
López-Domínguez et al PRD(06)ht [Schwarzschild,
and thermodynamics]; Dolan et al CQG(07)
[BTZ, and discrete time]; Chaichian et al PLB(08)-a0710,
Kobakhidze PRD(09)-a0712 [corrections
to Schwarzschild]; 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]; > s.a. black-hole
radiation; schwarzschild solution.
@ Cosmology: Marcolli & Pierpaoli a0908 [early
universe]; > s.a. friedmann
equation; inflation; non-commutative
physics.
@ Related topics: Rivelles AIP(05)ht/04 [and
Seiberg-Witten map]; Zupnik CQG(07)
[reality]; > s.a. Star Product.
Quantum Gravity > s.a. discrete
models; photons in quantum gravity.
@ General references: Moffat PLB(00)ht, PLB(00)ht [perturbative];
Vassilevich NPB(02)
[2D, Moyal];
Pimentel & Mora GRG(05)gq/04 [string
theory quantum cosmology]; Heller et al IJTP(05)gq, GRG(04)gq/05, JMP(05);
Martinetti MPLA(05)gq-in
[and thermal time hypothesis];
Aastrup & Grimstrup IJMPA(07)ht/06,
Chamseddine & Connes PRL(07)
[boundary terms from spectral action], a0812 [introduction
and overview].
@ And lqg: Aastrup et al CQG(09)-a0802, JNCG(09)-a0802, CQG(09)-a0902-in.
@ Bianchi I models: Guzmán et al IJMPD(07);
Socorro et al IJTP-a0910 [with
scalar, 
and
fluid]; > s.a. bianchi-I
models [Kasner].
@ Kantowski-Sachs models: García-Compeán et al PRL(02),
Barbosa & Pinto-Neto PRD(04)ht.
@ Other quantum cosmology: Vakili et al CQG(07)gq; Agüero
et al IJTP(07)gq [Bianchi
II]; Zejak & Dragovich a0708 [minisuperspace];
Fabi
et al PRD(08)-a0808 [corrections
to FRW metrics]; Bastos et al PRD(08)-a0712, a0904-in
[phase-space
non-commutative]; Mena et al IJMPD(09)
[WKB-type approximation]; > s.a. bianchi IX
models; friedmann
equation; relativistic
cosmology; quantum cosmology.
@ 3D: Schroers PoS-a0710 [phase-space
non-commutativity]; > 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 gq/97, 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.
Other Aspects
@ Large extra dimensions: Lizzi et al MPLA(01)ht/00 [Randall-Sundrum].
main page – abbreviations – journals – comments – other
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send feedback and suggestions to bombelli at olemiss.edu – modified 13
nov
2009