An Invariant Action for Noncommutative Gravity in Four-Dimensions

Abstract

Two main problems face the construction of noncommutative actions for gravity with star products: the complex metric and finding an invariant measure. The only gauge groups that could be used with star products are the unitary groups. I propose an invariant gravitational action in D=4 dimensions based on the constrained gauge group U(2,2) broken to $U(1,1)\times U(1,1).$ No metric is used, thus giving a naturally invariant measure. This action is generalized to the noncommutative case by replacing ordinary products with star products. The four dimensional noncommutative action is studied and the deformed action to first order in deformation parameter is computed.

11 pages. Paper shortened. Consideration is now limited to gravity in four-dimensions

References in corpus (6)

• Noncommutative finite-dimensional manifolds. I. Spherical manifolds and related examples
• Covariant Coordinate Transformations on Noncommutative Space
• Noncommutative Gravity in two Dimensions
• Gravitational fields on a noncommutative space
• Noncommutative Einstein-AdS Gravity in three Dimensions
• Teleparallel Complex Gravity as Foundation for Noncommutative Gravity

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