Type N Einstein space Time Machine spacetime

We present an Einstein space axially symmetry spacetime admitting closed timelike curves (CTCs) which appear after a certain instant of time, i.e., a time machine spacetime. The spacetime is a four-dimensional generalization of flat Misner space in curved spacetime, free-from curvature divergences and belongs to type N in the Petrov classification. The spacetime admits a non-expanding, non-twisting, and shear-free null geodesic congruence.