GLOBAL VORTEX AND BLACK COSMIC-STRING

We study global vortices coupled to (2+1)-dimensional gravity with a n egative cosmological constant. We found nonsingular vortex solutions i n phi(4) theory with a broken U(1) symmetry, of which the spacetimes d o 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 hy perbola; however, it becomes a charged black hole when the magnitude o f the cosmological constant is less than the critical value. We explai n through a duality transformation the reason why a static global vort ex which is electrically neutral forms a black hole with electric char ge. Under the present experimental bound of the cosmological constant, implications for cosmology as st straight black cosmic string are als o discussed in comparison with a global U(1) cosmic string in the spac etime of the zero cosmological constant. [S0556-2821(97)02324-2].