Stability Conditions For a Noncommutative Scalar Field Coupled to Gravity

We consider a noncommutative scalar field with a covariantly constant noncommutative parameter in a curved space-time background. For a potential as a noncommutative polynomial it is shown that the stability conditions are unaffected by the noncommutativity, a result that is valid irrespective whether space-time has horizons or not.Comment: 12 pages. Version to match the one to appear in Physics Letters