Obstructions to the existence of static cosmic strings in an Abelian Higgs model

There are obstructions in the Bogomol'nyi critical phase to the existence of a cylindrically symmetric cosmic string solution of the Einstein equations coupled with the Abelian Higgs model. In the compact case, the obstruction is exact, which forbids the presence of gravitational condensates and leads to the quantization of the energy scale of symmetry breaking. In the noncompact case, the obstruction is an inequality which says that, at a given level of broken symmetry, the topological charge or winding number of a string cannot be too large in order to maintain finite energy.