A stationary cylindrically symmetric spacetime which admits CTCs and its physical interpretation

Here we present a stationary cylindrically symmetric spacetime which is free from curvature divergence, and satisfy pure radiation field as matter-energy content with positive constant energy density. The metric admits circular closed timelike curves (CTCs) everywhere outside a finite region and the stability of these curves under small linear perturbations is studied, and found to be linearly stable. The metric is of type N in the Petrov classification scheme, and it has a shearfree geodesic null congruence. The physical interpretation of this solution, based on the study of the equation of the geodesic deviation, will be presented. It is demonstrated that, this solution can be understood as exact transverse gravitational waves with amplitudes Ψ4.