Gauging the twisted Poincare symmetry as noncommutative theory of gravitation

TL;DR

This paper proposes a gauge theory formulation of noncommutative gravity based on twisted Poincare symmetry, aiming to incorporate noncommutative space-time effects into a covariant gravitational framework.

Contribution

It introduces a novel gauge theory approach to noncommutative gravity that maintains covariance under general coordinate transformations.

Findings

Formulation of noncommutative gravity using twisted Poincare symmetry.

Discussion of advantages and problems of the proposed approach.

Outline of potential solutions to related issues.

Abstract

Einstein's Theory of General Relativity was formulated as a gauge theory of Lorentz symmetry by Utiyama in 1956, while the Einstein-Cartan gravitational theory was formulated by Kibble in 1961 as the gauge theory of Poincare transformations. In a noncommutative space-time with canonical commutation relations between the coordintes, Lorentz symmetry is violated and field theories constructed on such space-times have instead the so-called twisted Poincare invariance. In this paper a gauge theory formulation of noncommutative gravity is proposed based on the twisted Poincare symmetry together with the requirement of covariance under the general coordinate transformations, an essential ingredient of the theory of general relativity. The advantages of such a formulation as well as the related problems are discussed and possible ways out are outlined.