A Numerical Exploration of the Spherically Symmetric SU(2) Einstein-Yang-Mills Equations

TL;DR

This paper numerically explores the most general spherically symmetric Einstein-Yang-Mills equations with SU(2) gauge group, discovering new static solutions and non-universal critical phenomena beyond the magnetic ansatz.

Contribution

It relaxes the magnetic ansatz in Einstein-Yang-Mills equations, revealing new solutions and critical behaviors through advanced numerical methods.

Findings

Discovered new static solutions not asymptotically flat.

Identified non-universal type II critical solutions.

Developed a novel adaptive mesh refinement code.

Abstract

The Einstein-Yang-Mills equations are the source of many interesting solutions within general relativity, including families of particle-like and black hole solutions, and critical phenomena of more than one type. These solutions, discovered in the last thirty years, all assume a restricted form for the Yang-Mills gauge potential known as the "magnetic" ansatz. In this thesis we relax that assumption and investigate the most general solutions of the Einstein-Yang-Mills system assuming spherically symmetry, a Yang-Mills gauge group of SU(2), and zero cosmological constant. We proceed primarily by numerically integrating the equations and find new static solutions, for both regular and black hole boundary conditions, which are not asymptotically flat, and attempt to classify the possible static behaviours. We develop a code to solve the dynamic equations that uses a novel adaptive mesh refinement algorithm making full use of double-null coordinates. We find that the "type II" critical behaviour in the general case exhibits non-universal critical solutions, in contrast to the magnetic case and to all previously observed type II critical behaviour.