Classical solutions of the gravitating Abelian Higgs model - art. no. 085004

We consider the classical equations of the gravitating Abelian-Higgs model in an axially symmetric ansatz. Several properties of the solutions (the Me lvin branch and the string branch) of these equations are presented. These solutions are also constructed for winding numbers n=2. It is shown that th ese gravitating vortices exist in attractive and repulsive phases, separate d by the value of the Higgs coupling constant parameter leading to self-dua l equations.