Noncommutative Geometry and Gravity

Details Noncommutative Geometry and Gravity Noncommutative Geometry and Gravity

2005-10-06

arxiv.org/abs/hep-th/0510059v2

Class.Quant.Grav. 23 (2006) 1883-1912

Physics

High Energy Physics

High Energy Physics - Theory

40pages; v2: references added

Scientific paper

10.1088/0264-9381/23/6/005

We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star-product. The class of noncommutative spaces studied is very rich. Non-anticommutative superspaces are also briefly considered. The differential geometry developed is covariant under deformed diffeomorphisms and it is coordinate independent. The main target of this work is the construction of Einstein's equations for gravity on noncommutative manifolds.

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