Cylindrical-spherical solitonic waves and cosmic strings

Abstract

We present a family of solutions of the Einstein equations, corresponding to a single soliton perturbation of a flat seed metric, obtained applying Alekseev's inverse scattering method. The solitonic perturbations differ from most solutions previously presented in that they correspond 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 introduction 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 in the width of the solitonic wave leads to an impulsive wave solution that has elsewhere been interpreted as related to the emission of gravitational radiation associated to a topological string breaking process.