Nonstationary Einstein-Maxwell fields interacting with a superconducting cosmic string

Abstract

Nonstationary cylindrically symmetric exact solutions of the Einstein-Maxwell equations are derived as single soliton perturbations of a Levi-Cività metric, by an application of the Alekseev inverse scattering method. We show that the metric derived by Witten, interpreted as describing the electrogravitational field of a straight, stationary, conducting wire, may be recovered in the limit of a “wide” soliton. This leads to the possibility of interpreting the solitonic solutions as representing a nonstationary electrogravitational field exterior to, and interacting with, a thin, straight, superconducting cosmic string. We give a detailed discussion of the restrictions that arise when appropriate energy and regularity conditions are imposed on the matter and fields comprising the string, considered as the “source,” the most important being that this “source” must necessarily have a nonvanishing minimum radius. We show that, as a consequence, it is not possible, except in the stationary case, to assign uniquely a current to the source from knowledge of the electrogravitational fields outside the source. A discussion of the asymptotic properties of the metrics and the physical meaning of their curvature singularities, as well as that of some of the metric parameters, is also included.

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