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
EH 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.
@ 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 and
ht/06-in
[deformed diffeomorphisms]; Calmet & Kobakhidze PRD(05)ht [general
relativity]; Kobakhidze ht/06;
Harikumar & Rivelles CQG(06)ht [and
non-associative]; Mukherjee & Saha PRD(06)
[non-commutative corrections]; Fucci & Avramidi a0708 [non-commutative
Einstein equation].
@ 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].
@ From string theory: Álvarez-Gaumé et al NPB(06).
@ From other theories: Yang ht/06,
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 a0710,
Kobakhidze a0712 [corrections
to Schwarzschild]; Mukherjee & Saha a0710 [corrections
to Reissner-Nordström]; Chaichian et al JHEP(08)
[including cosmological constant]; Nicolini a0807 [rev].
@ Related topics: Rivelles ht/04-in
[and Seiberg-Witten map]; Zupnik CQG(07)
[reality].
> Phenomenology: see black
hole
radiation; inflation; non-commutative
physics [cosmology]; schwarzschild solution.
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,
Aastrup et al a0802, a0802 [and
lqg]; Chamseddine & Connes PRL(07)
[boundary terms from spectral action].
@ Quantum cosmology: García-Compeán et al PRL(02),
Barbosa & Pinto-Neto PRD(04)ht [Kantowski-Sachs];
Vakili et al CQG(07)gq;
Guzmán et al IJMPD(07)
[Bianchi I]; Agüero et al IJTP(07)gq [Bianchi
II]; Zejak Dragovich a0708 [minisuperspace]; > s.a. bianchi
I [Kasner], relativistic
cosmology, quantum cosmology.
@ 3D: Schroers a0710-in;
> 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
sites – Acknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified
14 jul 2008