Complete Classification of the String-like Solutions of the Gravitating Abelian Higgs Model

The static cylindrically symmetric solutions of the gravitating Abelian Higgs model form a two parameter family. In this paper we give a complete classification of the string-like solutions of this system. We show that the parameter plane is composed of two different regions with the following characteristics: One region contains the standard asymptotically conic cosmic string solutions together with a second kind of solution with Melvin-like asymptotic behavior. The other region contains two types of solutions with bounded radial extension. The border between the two regions is the curve of maximal angular deficit of (Formula presented)