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In this paper, we will study non-commutative corrections in the metric tensorfor the G\"{o}del-type universe, a model that has as its main characteristicthe possibility of violation of causality, allowing therefore time travel. Wealso find that the critical radius in such a model, which eventually willdetermine the time travel possibility, is modified due to the non commutativityof spatial coordinates.

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