On the existence of soliton and hairy black hole solutions of su(N) Einstein-Yang-Mills theory with a negative cosmological constant

TL;DR

This paper proves the existence of non-trivial soliton and black hole solutions in su(N) Einstein-Yang-Mills theory with a negative cosmological constant, highlighting solutions with zero gauge field functions and potential stability.

Contribution

It demonstrates the existence of solutions for any N with all gauge functions zero, especially under large negative cosmological constant, extending previous results in Einstein-Yang-Mills theory.

Findings

Existence of solutions for any N with N-1 gauge degrees of freedom.

Solutions with all gauge functions having no zeros.

Potential linear stability of some solutions.

Abstract

We study the existence of soliton and black hole solutions of four-dimensional su(N) Einstein-Yang-Mills theory with a negative cosmological constant. We prove the existence of non-trivial solutions for any integer N, with N-1 gauge field degrees of freedom. In particular, we prove the existence of solutions in which all the gauge field functions have no zeros. For fixed values of the parameters (at the origin or event horizon, as applicable) defining the soliton or black hole solutions, if the magnitude of the cosmological constant is sufficiently large, then the gauge field functions all have no zeros. These latter solutions are of special interest because at least some of them will be linearly stable.