Global Vortex and Black Cosmic String

TL;DR

This paper investigates global vortex solutions in (2+1)D gravity with negative cosmological constant, revealing conditions under which they form regular spacetimes or charged black holes, with implications for cosmology.

Contribution

It presents new nonsingular vortex solutions coupled to (2+1)D gravity with negative cosmological constant and explains their black hole formation via duality transformation.

Findings

Nonsingular vortex solutions without curvature singularity.

Spacetime structure depends on the cosmological constant magnitude.

Global vortices can form charged black holes under certain conditions.

Abstract

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.