On some models of geometric noncommutative general relativity

Abstract

Using Fedosov theory of deformation quantization of endomorphism bundle we construct several models of pure geometric, deformed vacuum gravity, corresponding to arbitrary symplectic noncommutativity tensor. Deformations of Einstein-Hilbert and Palatini actions are investigated. Coordinate covariant field equations are derived up to the second order of the deformation parameter. For some models they are solved and explicit corrections to an arbitrary Ricci-flat metric are pointed out. The relation to the theory of Seiberg-Witten map is also studied and the correspondence to the spacetime noncommutativity described by Fedosov *-product of functions is explained.

arXiv comment26 pages, rearranged, new references added. To appear in Phys. Rev. D

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• Noncommutative Electrodynamics from $SO(2,3{)}_{\star }$ Model of Noncommutative Gravity
• Dirac field and gravity in NC $SO(2,3{)}_{\star }$ model
• Background independent noncommutative gravity from Fedosov quantization of endomorphism bundle
• Canonical Deformation of $N=2$ $Ad{S}_4$ SUGRA
• Noncommutative $SO(2,3{)}_{\star }$ Gauge Theory of Gravity
• Field Theory with Coordinate Dependent Noncommutativity
• Remarks on generalized Fedosov algebras
• Noncommutative $D=5$ Chern-Simons Gravity: Kaluza-Klein Reduction and Chiral Gravitational Anomaly