Ricci flows, wormholes and critical phenomena

TL;DR

This paper investigates how wormhole geometries evolve under Ricci flow, revealing critical phenomena similar to gravitational collapse, with numerical methods applicable to matter-coupled Ricci flows in string theory.

Contribution

It demonstrates the existence of critical phenomena in Ricci flow evolution of wormholes and space bubbles, using numerical methods applicable to matter-coupled flows.

Findings

Wormhole throats either pinch off or grow monotonically depending on initial data.

A critical transition between these behaviors exhibits phenomena similar to gravitational collapse.

Numerical methods are applicable to matter-coupled Ricci flows in string theory.

Abstract

We study the evolution of wormhole geometries under Ricci flow using numerical methods. Depending on values of initial data parameters, wormhole throats either pinch off or evolve to a monotonically growing state. The transition between these two behaviors exhibits a from of critical phenomena reminiscent of that observed in gravitational collapse. Similar results are obtained for initial data that describe space bubbles attached to asymptotically flat regions. Our numerical methods are applicable to "matter-coupled" Ricci flows derived from conformal invariance in string theory.