  We study global vortices coupled to (2+1) dimensional gravity with negative
cosmological constant. We found nonsingular vortex solutions in $\phi^4$-theory
with a broken U(1) symmetry, of which the spacetimes do not involve physical
curvature singularity. When the magnitude of 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 cosmological constant is less than the critical value. We
explain through duality transformation the reason why static global vortex
which is electrically neutral forms black hole with electric charge. Under the
present experimental bound of the cosmological constant, implications on
cosmology as a straight black cosmic string is also discussed in comparison
with global U(1) cosmic string in the spacetime of the zero cosmological
constant.
