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 Pleba\'nski action is explicitly obtained. 
S. Estrada-Jimenez, H. Garcia-Compean, O. Obregon, C. Ramirez