Critical Collapse of Skyrmions

TL;DR

This paper investigates gravitational collapse of spherically symmetric skyrmions, revealing static sphaleron solutions as critical points and identifying a new first order phase transition where subcritical data evolve into stable solutions.

Contribution

It introduces a novel type of first order phase transition in skyrmion collapse, showing static sphalerons as critical solutions and detailing the evolution near criticality.

Findings

Static sphaleron solutions act as critical points.

Subcritical data can evolve into stable solutions.

Near-critical solutions follow the unstable manifold.

Abstract

We study first order phase transitions in the gravitational collapse of spherically symmetric skyrmions. Static sphaleron solutions are shown to play the role of critical solutions separating black-hole spacetimes from no-black-hole spacetimes. In particular, we find a new type of first order phase transition where subcritical data do not disperse but evolve towards a static regular stable solution. We also demonstrate explicitly that the near-critical solutions depart from the intermediate asymptotic regime along the unstable manifold of the critical solution.