A family of type N space-time with a negative cosmological constant and causality violation - Ahmed, Faizuddin (Progress of theoretical and experimental physics, 2019)
Abstract A family of type N exact solutions of the Einstein’s field equations with non-zero cosmological constant admitting closed time-like curves, which appear after a certain instant of time, is presented. The space-time is free from curvature divergence, admits a non-expanding, non-twisting, and shear-free geodesics null congruence, and belongs to a special class of type N Kundt metrics. The space-time exhibits geometrically different properties from the known plane-fronted gravitational waves with parallel rays (pp-waves) or plane waves which violate the causality condition. This family of solutions is a four-dimensional generalization of the two-dimensional Misner space metric in curved space-time.