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arXiv · 0709.0015

Noncommutative Einstein Equations

Guglielmo Fucci·Ivan G. Avramidi
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Abstract

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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Guglielmo Fucci, Ivan G. Avramidi. 2007-09-04. Noncommutative Einstein Equations. https://doi.org/10.1088/0264-9381%2F25%2F2%2F025005

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