Non stationary Einstein-Maxwell fields interacting with a superconducting cosmic string

TL;DR

This paper derives exact non-stationary solutions to Einstein-Maxwell equations representing interactions between electromagnetic fields and a superconducting cosmic string, extending previous stationary models and analyzing their physical properties.

Contribution

It introduces novel non-stationary Einstein-Maxwell solutions as soliton perturbations of Levi-Civita metrics, modeling dynamic electrogravitational interactions with superconducting cosmic strings.

Findings

Solutions recover stationary Witten metric in the wide soliton limit.

Non-uniqueness of current assignment outside the source in non-stationary cases.

Restrictions on matter and field configurations due to energy and regularity conditions.

Abstract

Non stationary cylindrically symmetric exact solutions of the Einstein-Maxwell equations are derived as single soliton perturbations of a Levi-Civita metric, by an application of Alekseev inverse scattering method. We show that the metric derived by L. 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 non stationary electrogravitational field exterior to, and interacting with, a thin, straight, superconducting cosmic string. We give a detailed discussion of the restrictions that arise when appropiate energy and regularity conditions are imposed on the matter and fields comprising the string, considered as `source', the most important being that this `source' must necessarily have a non- vanishing 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 a knowledge of the electrogravitational fields outside the source. A discussion of the asymptotic properties of the metrics, the physical meaning of their curvature singularities, as well as that of some of the metric parameters, is also included.