On Non-Commutative Correction of the G\"odel-type Metric

In this paper, we will study non-commutative corrections in the metric tensor for the G"{o}del-type universe, a model that has as its main characteristic the possibility of violation of causality, allowing therefore time travel. We also find that the critical radius in such a model, which eventually will determine the time travel possibility, is modified due to the non commutativity of spatial coordinates.