Existence of global strings coupled to gravity

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Abstract
We consider σ-model strings and U(1) global strings coupled to gravity and look for static solutions with whole-cylinder symmetry. We prove that in both cases there are no regular spatially compact solutions. The U(1) global string admits no asymptotically well-behaved solutions, whereas σ-model strings can be constructed under certain assumptions. Finally we present some singular solutions and show that one of them corresponds to a physical global string.

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