Classical solutions of the gravitating Abelian Higgs model

Abstract

We consider the classical equations of the gravitating Abelian-Higgs model in an axially symmetric ansatz. Several properties of the solutions (the Melvin branch and the string branch) of these equations are presented. These solutions are also constructed for winding numbers $n=2.\mathrm{}$ It is shown that these gravitating vortices exist in attractive and repulsive phases, separated by the value of the Higgs coupling constant parameter leading to self-dual equations.