Noncommutative Einstein Equations

Details Noncommutative Einstein Equations Noncommutative Einstein Equations

2007-08-31

arxiv.org/abs/0709.0015v2

Class.Quant.Grav.25:025005,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 Pages, LaTeX, reference added

Scientific paper

10.1088/0264-9381/25/2/025005

We study a noncommutative deformation of general relativity where the gravitational field is described by a matrix-valued symmetric two-tensor field. The equations of motion are derived in the framework of this new theory by varying a diffeomorphisms and gauge invariant action constructed by using a matrix-valued scalar curvature. Interestingly the genuine noncommutative part of the dynamical equations is described only in terms of a particular tensor density that vanishes identically in the commutative limit. A noncommutative generalization of the energy-momentum tensor for the matter field is studied as well.

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