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Noncommutative Gravity Solutions

We consider noncommutative geometries obtained from a triangular Drinfeld twist and review the formulation of noncommutative gravity. A detailed study of the abelian twist geometry is presented, including the fundamental theorem of noncommutative Riemannian geometry. Inspired by [1, 2], we obtain solutions of noncommutative Einstein equations by considering twists that are compatible with the curved spacetime metric.