Gravity in Non-Commutative Geometry

Abstract

We study general relativity in the framework of non-commutative differential geometry. In particular, we introduce a gravity action for a space-time which is the product of a four dimensional manifold by a two-point space. In the simplest situation, where the Riemannian metric is taken to be the same on the two copies of the manifold, one obtains a model of a scalar field coupled to Einstein gravity. This field is geometrically interpreted as describing the distance between the two points in the internal space.

ZU-TH-30/1992 and ETH/TH/92/44, 11 pages. (The earlier version of this paper was the incomplete and unedited file which accidently replaced the corrected file)

References in corpus (2)

• Grand Unification in Non-Commutative Geometry
• Some Elements of Connes' Non-Commutative Geometry, And Space-Time Geometry

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