On some models of geometric noncommutative general relativity

Details On some models of geometric noncommutative general relativity On some models of geometric noncommutative general relativity

2010-10-31

arxiv.org/abs/1011.0165v2

Phys.Rev.D84:065005,2011

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1103/PhysRevD.84.065005

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.

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