Axisymmetric Pure Radiation Space-Time with Causality-Violating Geodesics

We present a stationary axisymmetric space-time admitting circular closed timelike geodesics everywhere within a finite region of space. The space-time is free from curvature divergence and is locally isometric to a nonvacuum pp-wave space-time. The matter-energy content is a pure radiation field and satisfies the null energy condition (NEC), and the metric is of type N in the Petrov classification scheme. Finally, we demonstrate the existence of timelike and null circular geodesic paths for this metric.