  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.
