WORMHOLE AT THE CORE OF AN INFINITE COSMIC-STRING

We study a solution of Einstein's equations that describes a straight cosmic string with a variable angular deficit, starting with a 2 pi de ficit at the core. We show that the coordinate singularity associated with this defect can be interpreted as a traversable wormhole lodging at the core of the string. A negative energy density gradually decreas es the angular deficit as the distance from the core increases, ending , at radial infinity, in a Minkowski spacetime. The negative energy de nsity can be confined to a small transversal section of the string by gluing to it an exterior Gott-like solution that freezes the angular d eficit existing at the matching border. The equation of state of the s tring is such that any massive particle may stay at rest anywhere in t his spacetime. In this sense this is a 2+1 spacetime solution. A gener alization that includes the existence of two interacting parallel worm holes is displayed. These wormholes an not traversable. Finally, we po int out that a similar result, flat at infinity and with a 2 pi defect (or excess) at the core, has been recently published by Dyer and Marl eau. Even though theirs is a local string fully coupled to gravity, ou r toy model captures important aspects of this solution. [S0556-2821(9 7)03422-X].