Noncommutative deformation of four dimensional Einstein gravity

Abstract

We construct a model for noncommutative gravity in four dimensions, which reduces to the Einstein-Hilbert action in the commutative limit. Our proposal is based on a gauge formulation of gravity with constraints. While the action is metric independent, the constraints insure that it is not topological. We find that the choice of the gauge group and of the constraints are crucial to recover a correct deformation of standard gravity. Using the Seiberg-Witten map the whole theory is described in terms of the vierbeins and of the Lorentz transformations of its commutative counterpart. We solve explicitly the constraints and exhibit the first order noncommutative corrections to the Einstein-Hilbert action.

LaTex, 11 pages, comments added, to appear in Classical and Quantum Gravity

References in corpus (4)

• Three-dimensional Noncommutative Gravity
• Noncommutative Gravity in two Dimensions
• Noncommutative Einstein-AdS Gravity in three Dimensions
• Noncommutative AdS Supergravity in three Dimensions

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