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] and [2], we obtain solutions of noncommutative Einstein equations by considering twists that are compatible with the curved spacetime metric.