Spacetime structure of the global vortex

TL;DR

This paper investigates the spacetime geometry of global vortices across multiple dimensions, revealing their compactification effects and implications for extra-dimensional hierarchy resolution.

Contribution

It provides a detailed analysis of the global vortex's spacetime structure, including maximal extensions and bounds for solutions with strong gravity effects.

Findings

Vortices cause space to compactify at the Hubble scale.

Derived bounds on the existence of strongly gravitating vortices.

Discussed relevance to hierarchy problem in extra dimensions.

Abstract

We analyse the spacetime structure of the global vortex and its maximal analytic extension in an arbitrary number of spacetime dimensions. We find that the vortex compactifies space on the scale of the Hubble expansion of its worldvolume, in a manner reminiscent of that of the domain wall. We calculate the effective volume of this compactification and remark on its relevance to hierarchy resolution with extra dimensions. We also consider strongly gravitating vortices and derive bounds on the existence of a global vortex solution.