CYLINDRICAL SPHERICAL SOLITONIC WAVES AND COSMIC STRINGS

We present a family of solutions of the Einstein equations, correspond ing to a single soliton perturbation of a flat seed metric, obtained a pplying Alekseev's inverse scattering method. The solitonic perturbati ons differ from most solutions previously presented in that they corre spond to gravitational waves which, in Marder's terminology, possess a cylindrical-spherical structure and therefore have spacelike sections of finite extent. The solutions obtained are locally (quasi) regular everywhere, and, in a sense specified in the text, asymptotically flat . However, because of the presence of a pair of ring-like structures, the geometrical interpretation of the metrics requires the introductio n of a non-trivial topology, in the form of two 'universes', connected smoothly through the rings, in a manner already familiar from similar analyses for the Kerr metric and Appell rings. An appropriate limit i n the width of the solitonic wave leads to an impulsive wave solution that has elsewhere been interpreted as related to the emission of grav itational radiation associated to a topological string breaking proces s.