Some Remarks on Gravity in Noncommutative Spacetime and a New Solution to the Structure Equations

Details Some Remarks on Gravity in Noncommutative Spacetime and a New Solution to the Structure Equations Some Remarks on Gravity in Noncommutative Spacetime and a New Solution to the Structure Equations

2003-03-14

arxiv.org/abs/hep-th/0303128v1

Physics

High Energy Physics

High Energy Physics - Theory

19 pages

Scientific paper

In this paper, starting from the common foundation of Connes' noncommutative geometry (NCG) [1,2,3,4], various possible alternatives in the formulation of a theory of gravity in noncommutative spacetime are discussed in detail. The diversity in the final physical content of the theory is shown to the the consequence of the arbitrariness in each construction steps. As an alternative in the last step, when the staructure equations are to be solved, a minimal set of constraints on the torsion and connection is found to determine all the geometric notions in terms of metric. In the Connes-Lott model of noncommutative spacetime, in order to keep the full spectrum of the discretized Kaluza-Klein theory [5], it is necessary to include the torsion in the generalized Einstein-Hilbert-Cartan action.

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