Weak-field gravity of circular cosmic strings

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Abstract
A weak-field solution of Einstein's equations is constructed. It is generated by a circular cosmic string externally supported against collapse. The solution exhibits a conical singularity, and the corresponding deficit angle is the same as for a straight string for the same linear energy density. This confirms the deficit-angle assumption made in the Frolov-Israel-Unruh derivation of the metric describing a string loop at a moment of time symmetry.
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