Global vortex and black cosmic string

We study global vortices coupled to (2+1)-dimensional gravity with a negative cosmological constant. We found nonsingular vortex solutions in [Formula presented] theory with a broken U(1) symmetry, of which the spacetimes do not involve a physical curvature singularity. When the magnitude of a negative cosmological constant is larger than a critical value at a given symmetry breaking scale, the spacetime structure is a regular hyperbola; however, it becomes a charged black hole when the magnitude of the cosmological constant is less than the critical value. We explain through a duality transformation the reason why a static global vortex which is electrically neutral forms a black hole with electric charge. Under the present experimental bound of the cosmological constant, implications for cosmology as a straight black cosmic string are also discussed in comparison with a global U(1) cosmic string in the spacetime of the zero cosmological constant. © 1997 The American Physical Society.