REGULAR CYLINDRICALLY SYMMETRICAL EINSTEIN-MAXWELL METRICS OF PETROV TYPE-D

We analyse all presently known exact solutions of the vacuum Einstein and Einstein-Maxwell equations sharing the properties of being of Petrov type D, non-stationary, cylindrically symmetric, asymptotically flat and regular everywhere. All these solutions are particular subfamilies of a general one that describes the evolution of a single solitonic perturbation travelling on a flat spacetime background. We also investigate the relationship between these solitonic-type families and analytic extensions from stationary families. In particular we reobtain the Piran, Safier and Katz solution by performing an analytic extension from the massless Kerr-NUT spacetime.