Interaction of Einstein-Maxwell radiation and a cosmic string: Special solutions with hypersurface-orthogonal Killing vectors.

Abstract

We present several nontrivial limits of a new family of exact solutions of the Einstein-Maxwell equations for axisymmetric nonstationary spacetimes, obtained using Alekseev's inverse-scattering method, which we previously interpreted as describing the presence of a rotating cosmic string interacting with electromagnetic and gravitational radiation. The limit in which the {ital C} energy of the solutions goes to infinity is related to a change in their geometry, reminiscent of some results recently found for both gauge and global cosmic strings. The axisymmetry, i.e., the presence of a (quasiregular) symmetry axis,'' is in general lost, except in one case, which includes hypersurface-orthogonal Killing vectors. Its relation to Xanthopoulos's question as to whether the rotation'' can be stopped is discussed. This last case can also be interpreted as a collapsing Melvin electromagnetic universe. We also analyze a particular limit that leads to a vacuum solution with a curvature singularity on the symmetry axis, but asymptotically flat in the radial direction.