An equivalence theorem for string solutions of the Einstein matter-gauge equations (Q1202937)

The author studies static solutions to Einstein field equations for a self-gravitating complex scalar field minimally coupled to electromagnetism, representing finite energy cosmic string spacetimes. It is shown that in this class of solutions and when the two-dimensional Riemannian manifold in which the strings reside is either compact or asymptotically Euclidean, the field equations are equivalent to a system of Einstein-Bogomol'nyj equations. Then it is proven that within this class of solutions the string manifold cannot be both conformally and asymptotically Euclidean.