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.

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

References in corpus (16)

• A Gravity Theory on Noncommutative Spaces
• Corrections to Schwarzschild Solution in Noncommutative Gauge Theory of Gravity
• Second Order Noncommutative Corrections to Gravity
• Noncommutative D=4 gravity coupled to fermions
• A note on the noncommutative correction to gravity
• Noncommutative Gravity Solutions
• Lie algebraic Noncommutative Gravity
• Deformed Reissner--Nordstrom solutions in noncommutative gravity
• Twisted Covariant Noncommutative Self-dual Gravity
• Covariant Star Product for Exterior Differential Forms on Symplectic Manifolds
• Noncommutative gauge theory using covariant star product defined between Lie-valued differential forms
• SL(2,C) gravity on noncommutative space with Poisson structure
• Tensor calculus on noncommutative spaces
• U(2,2) gravity on noncommutative space with symplectic structure
• Seiberg-Witten equations from Fedosov deformation quantization of endomorphism bundle
• The Fedosov deformation quantization for some induced symplectic connection

Cited by in corpus (11)

• NC $SO(2,3{)}_{\star }$ gravity: noncommutativity as a source of curvature and torsion
• Gauge theories on quantum spaces
• Noncommutative gravity with self-dual variables
• 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