Dyons and dyonic black holes in ${\mathfrak {su}}(N)$ Einstein-Yang-Mills theory in anti-de Sitter space-time

TL;DR

This paper introduces new spherically symmetric dyonic black hole and soliton solutions in ${\mathfrak {su}}(N)$ Einstein-Yang-Mills theory within anti-de Sitter space, revealing a rich phase space with potential stability for nodeless solutions.

Contribution

It provides the first detailed exploration of dyonic solutions in ${\mathfrak {su}}(N)$ Einstein-Yang-Mills theory in AdS space, including solutions with no magnetic gauge field zeros.

Findings

Rich phase space with solutions having over fifty zeros in magnetic functions.

Existence of nodeless solutions when the cosmological constant is sufficiently large.

Conjecture that some nodeless solutions may be linearly stable.

Abstract

We present new spherically symmetric, dyonic soliton and black hole solutions of the ${\mathfrak {su}}(N)$ Einstein-Yang-Mills equations in four-dimensional asymptotically anti-de Sitter space-time. The gauge field has nontrivial electric and magnetic components and is described by $N-1$ magnetic gauge field functions and $N-1$ electric gauge field functions. We explore the phase space of solutions in detail for ${\mathfrak {su}}(2)$ and ${\mathfrak {su}}(3)$ gauge groups. Combinations of the electric gauge field functions are monotonic and have no zeros; in general the magnetic gauge field functions may have zeros. The phase space of solutions is extremely rich, and we find solutions in which the magnetic gauge field functions have more than fifty zeros. Of particular interest are solutions for which the magnetic gauge field functions have no zeros, which exist when the negative cosmological constant has sufficiently large magnitude. We conjecture that at least some of these nodeless solutions may be stable under linear, spherically symmetric, perturbations.