Critical Behaviour in Gravitational Collapse of a Yang-Mills Field

TL;DR

This paper numerically investigates the critical phenomena in the gravitational collapse of a spherically symmetric SU(2) gauge field, revealing two distinct types of critical solutions with different black hole formation thresholds.

Contribution

It identifies and characterizes two different critical solutions in gravitational collapse, including a new transition scenario between discretely self-similar and static solutions.

Findings

Discretely self-similar critical solution allows arbitrarily small black holes.

Static Bartnik-McKinnon sphaleron critical solution leads to finite mass black holes.

Transition between the two critical behaviors is characterized by superposition.

Abstract

We present results from a numerical study of spherically-symmetric collapse of a self-gravitating, SU(2) gauge field. Two distinct critical solutions are observed at the threshold of black hole formation. In one case the critical solution is discretely self-similar and black holes of arbitrarily small mass can form. However, in the other instance the critical solution is the n=1 static Bartnik-Mckinnon sphaleron, and black hole formation turns on at finite mass. The transition between these two scenarios is characterized by the superposition of both types of critical behaviour.