Nonsingular global string compactifications

TL;DR

An exotic "compactification" of spacetime in which there are two infinite extra dimensions, using a global string instead of a domain wall is considered, and it is proved that a nonsingular static solution exists in the absence of a cosmological constant with a time-dependent metric.

Abstract

We consider an exotic `compactification' of spacetime in which there are two infinite extra dimensions, using a global string instead of a domain wall. By having a negative cosmological constant we prove the existence of a nonsingular static solution using a dynamical systems argument. A nonsingular solution also exists in the absence of a cosmological constant with a time-dependent metric. We compare and contrast this solution with the Randall-Sundrum universe and the Cohen-Kaplan spacetime, and consider the options of using such a model as a realistic resolution of the hierarchy problem.

Figures (1)

• Figure 1: A plot of the (x,y) phase plane. Critical points are marked with a dot and the invariant hyperboloid by the grey line. As $p$ varies the plot alters shape, but the qualitative features remain the same.