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In the 10-dimensional pp-waves background we have found using T-duality a 4-dimensional space-time in which closed time-like curves appear in the region bounded by two coaxial elliptic cylinders. This 4-dimensional space-time is similar to the Gödel-type space-time only in this region. Outside of this region the causal pathology does not appear.

Bounded region with closed time-like curves in T-dual pp-waves backgrounds