A note on the noncommutative correction to gravity
  An apparent contradiction in the leading order correction to noncommutative (NC) gravity reported in the literature has been pointed out. We show by direct computation that actually there is no such controvarsy and all perturbative NC corrections start from the second order in the NC parameter. The role of symmetries in the vanishing of the first order correction is manifest in our calculation. 
Pradip Mukherjee and Anirban Saha