Soliton and black hole solutions of su(N) Einstein-Yang-Mills theory in anti-de Sitter space

TL;DR

This paper introduces new soliton and black hole solutions in su(N) Einstein-Yang-Mills theory within anti-de Sitter space, highlighting their parameters, gauge field degrees of freedom, and potential stability.

Contribution

It provides explicit solutions for su(N) Einstein-Yang-Mills theory in anti-de Sitter space, analyzing their properties and stability prospects, especially for su(3) and su(4).

Findings

Solutions have N+1 parameters and N-1 gauge field degrees of freedom.

Existence of solutions with gauge functions having no zeros at large cosmological constant.

Some solutions are anticipated to be linearly stable.

Abstract

We present new soliton and hairy black hole solutions of su(N) Einstein-Yang-Mills theory in asymptotically anti-de Sitter space. These solutions are described by N+1 independent parameters, and have N-1 gauge field degrees of freedom. We examine the space of solutions in detail for su(3) and su(4) solitons and black holes. If the magnitude of the cosmological constant is sufficiently large, we find solutions where all the gauge field functions have no zeros. These solutions are of particular interest because we anticipate that at least some of them will be linearly stable.