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We consider the classical equations of the gravitating Abelian-Higgs model inan axially symmetric ansatz. More properties of the solutions of theseequations (the Melvin and the sting branches) are presented. These solutionsare also constructed for winding numbers N=2. It is shown that these vorticesexist in attractive and repulsive phases, separated by the value of the Higgscoupling constant parameter leading to self-dual equations.Comment: Latex, 10 pages, 10 figure

Classical solutions of the gravitating Abelian Higgs model