The Collapse of Large Extra Dimensions

TL;DR

This paper investigates the collapse of extra dimensions in higher-dimensional spacetime models, arguing that such collapse typically results in hidden singularities within black strings, thus preserving cosmic censorship.

Contribution

It provides a theoretical analysis and explicit initial data demonstrating the likelihood of singularity formation within black strings during extra dimension collapse.

Findings

Collapse leads to black string singularities

Naked singularities are likely avoided

Homogeneous extra dimensions collapse into hidden singularities

Abstract

In models of spacetime that are the product of a four-dimensional spacetime with an ``extra'' dimension, there is the possibility that the extra dimension will collapse to zero size, forming a singularity. We ask whether this collapse is likely to destroy the spacetime. We argue, by an appeal to the four-dimensional cosmic censorship conjecture, that--at least in the case when the extra dimension is homogeneous--such a collapse will lead to a singularity hidden within a black string. We also construct explicit initial data for a spacetime in which such a collapse is guaranteed to occur and show how the formation of a naked singularity is likely avoided.