Gravitational fields of straight and circular cosmic strings: Relation between gravitational mass, angular deficit, and internal structure

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Abstract
The first part of the paper formulates general conditions (independent of a particular gauge-theoretic model) under which a cylindrical distribution of matter can be joined to a vacuum exterior with a conical geometry and exhibits the relation between angular deficit and internal structure. To bring out the relation to gravitational mass, the second part is devoted to a detailed study of solutions of the initial-value problem for circular loops of string at a moment of time symmetry.

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