2-SOLITON SOLUTIONS OF THE EINSTEIN-MAXWELL-EQUATIONS

We present a family of solutions of the Einstein-Maxwell equations obt ained as a two-soliton transformation of a Minkowskian seed, using Ale kseev's inverse scattering method (AISM). For general values of the ar bitrary parameters that arise from the AISM, the metrics are of Petrov type I, and represent cylindrically symmetric perturbations of a coni cal spacetime ('thin cosmic string'), that preserve the asymptotic fla tness of the background, up to an additional deficit angle. The metric s can be made regular on the symmetry axis by an adequate choice of pa rameters. In the limit in which the C-energy goes to infinity, the met ric is singular, but can be 'renormalized', obtaining either (i) a fam ily of metrics where the symmetry axis contains a curvature singularit y, or (ii) a family of cylindrically symmetric metrics with a regular axis, that can be interpreted as simple solitonic perturbations of an unstable Melvin universe. These contain a subfamily of diagonal metric s. We include a comparison with other metrics, obtained as limiting ca ses and, in the case of vacuum solutions, we show, by an explicit calc ulation, that the results obtained are equivalent to the Belinski-Zakh arov transformation for two pairs of complex-conjugate soliton poles f or the same seed.