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An anti-de Sitter background four-dimensional type N solution of theEinstein's field equations, is presented. The matter-energy content pureradiation field satisfies the null energy condition (NEC), and the metric isfree-from curvature divergence. In addition, the metric admits a non-expanding,non-twisting and shear-free geodesic null congruence which is not covariantlyconstant. The space-time admits closed time-like curves which appear after acertain instant of time in a causally well-behaved manner. Finally, thephysical interpretation of the solution, based on the study of the equation ofthe geodesics deviation, is analyzed.

A type N radiation field solution with $\Lambda<0$ in a curved space-time and closed time-like curves