New exact solution describing the interaction of Einstein-Maxwell radiation and a rotating cosmic string

Abstract

We present a new family of exac solutions of the Einstein-Maxwell equations for cylindrically symmetric nonstationary space-times. The solutions can be interpreted as describing the presence of a rotating cosmic string interacting with electromagnetic and gravitational radiation. We show, by appropriate identifications, that our solutions include as subfamilies, and generalize, all the known results on this type of space-times recently obtained by Xanthopoulos and by Economou and Tsoubelis. We include also an analysis of the general structure of the solutions, the Maxwell and Weyl scalars and their asymptotic behavior. The solitonic behavior of the waves is depicted both in the form of a perturbation of the metric coefficients and as a nonvanishing flux of $C$ energy at null infinity. We also show that our solutions contain a subfamily with hypersurface-orthogonal Killing vectors. The metrics were obtained using Alekseev's inverse scattering method. Their relation with those obtained with other methods is briefly considered.