Gravity and the Structure of Noncommutative Algebras
  A gravitational field can be defined in terms of a moving frame, which when made noncommutative yields a preferred basis for a differential calculus. It is conjectured that to a linear perturbation of the commutation relations which define the algebra there corresponds a linear perturbation of the gravitational field. This is shown to be true in the case of a perturbation of Minkowski space-time. 
M. Buric, T. Grammatikopoulos, J. Madore and G. Zoupanos