Gravitating global defects: the gravitational field and compactification

TL;DR

This paper presents a method to incorporate the gravitational effects of global topological defects into Einstein's equations across multiple dimensions, revealing their role in creating deficit angles and facilitating spontaneous compactification.

Contribution

It introduces a general prescription for adding gravitational fields of global defects to Einstein's solutions with O(n) symmetry, linking defects to compactification mechanisms.

Findings

Global defects induce deficit solid angles in spacetime.

Scalar field configurations can cause spontaneous compactification of extra dimensions.

The method applies to solutions with O(n) symmetry in arbitrary dimensions.

Abstract

We give a prescription to add the gravitational field of a global topological defect to a solution of Einstein's equations in an arbitrary number of dimensions. We only demand that the original solution has a O(n) invariance with n greater or equal 3. We will see that the general effect of a global defect is to introduce a deficit solid angle. We also show how the same kind of scalar field configurations can be used for spontaneous compactification of "n" extra dimensions on an n-sphere.