A 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 $2 \pi$ deficit at the core. We show that the coordinate singularity associated to this defect can be interpreted as a traversible wormhole lodging at the the core of the string. A negative energy density gradually decreases the angular deficit as the distance from the core increases, ending, at radial infinity, in a Minkowski spacetime. The negative energy density can be confined to a small transversal section of the string by gluing to it an exterior Gott's like solution, that freezes the angular deficit existing at the matching border. The equation of state of the string is such that any massive particle may stay at rest anywhere in this spacetime. In this sense this is 2+1 spacetime solution.