Singular manifolds, topology change and the dynamics of compactification

TL;DR

This paper studies the dynamics of topology-changing transitions in compactified spacetimes with gravity, revealing scenarios of horizon formation or re-expansion, and proposing a new compactification mechanism linked to black-hole solutions.

Contribution

It demonstrates how gravitational dynamics influence topology change in compactified spaces and introduces a novel compactification mechanism based on black-hole asymptotics.

Findings

Horizon formation shields singularities during topology change.

Cycles either collapse into black holes or re-expand depending on initial conditions.

A new compactification mechanism is proposed using black-hole solutions.

Abstract

We investigate the dynamics of the geometric transitions associated to compactified spacetimes. By including the dynamics of gravity we are able to follow the evolution of collapsing cycles as they attempt to undergo a topology changing transition. Rather than achieving this singular geometry we find that one of two scenarios occur, depending on the initial conditions. Either a horizon forms, shielding a curvature singularity, or the cycle re-expands after an initial contraction phase. For the case where a horizon forms we identify the final state with a known analytic black-hole solution. We also show use our results to demonstate a novel compactification mechanism, owing to the asymptotic structure of this black-hole solution.