Gravity of superheavy higher-dimensional global defects

TL;DR

This paper investigates the gravitational properties of higher-dimensional global defects with a scalar field, revealing conditions for regular solutions and describing an analytic inflating defect model with a cigar-shaped extra dimension.

Contribution

It provides numerical solutions for higher-dimensional global defects and introduces an analytic inflating defect model with a cigar geometry in extra dimensions.

Findings

Low symmetry-breaking scales lead to flat worldsheet geometry.

High scales cause static solutions to become singular.

Inflating defect cores resolve singularities and exhibit cigar-shaped extra dimensions.

Abstract

Numerical solutions of Einstein's and scalar-field equations are found for a global defect in a higher-dimensional spacetime. The defect has a $(3+1)$-dimensional core and a ``hedgehog'' scalar-field configuration in $n=3$ extra dimensions. For sufficiently low symmetry-breaking scales $\eta$, the solutions are characterized by a flat worldsheet geometry and a constant solid deficit angle in the extra dimensions, in agreement with previous work. For $\eta$ above the higher-dimensional Planck scale, we find that static-defect solutions are singular. The singularity can be removed if the requirement of staticity is relaxed and defect cores are allowed to inflate. We obtain an analytic solution for the metric of such inflating defects at large distances from the core. The three extra dimensions of the nonsingular solutions have a ``cigar'' geometry. Although our numerical solutions were obtained for defects of codimension $n=3$, we argue that the conclusions are likely to apply to all $n\geq 3$.