Twisted covariant noncommutative self-dual gravity

A twisted covariant formulation of noncommutative self-dual gravity is presented. The formulation for constructing twisted noncommutative Yang-Mills theories is used. It is shown that the noncommutative torsion is solved at any order of the theta expansion in terms of the tetrad and some extra fields of the theory. In the process the first order expansion in theta for the Plebanski action is explicitly obtained.