Citation:Hughes, S. J., McManus, D. J. and Vandyck, M. A. (1993) 'Weak-field gravity of circular cosmic strings', Physical Review D, 47(2), 468-473 (6pp). doi: 10.1103/PhysRevD.47.468
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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