Monopoles, Dyons and Black Holes in the Four-Dimensional Einstein-Yang-Mills Theory

TL;DR

This paper explores a variety of monopole, dyon, and black hole solutions in four-dimensional Einstein-Yang-Mills theory with anti-de Sitter asymptotics, analyzing their structure, stability, and complex moduli space behavior.

Contribution

It provides a detailed classification and stability analysis of solutions, revealing a fractal moduli space as the cosmological constant tends to zero.

Findings

Existence of a continuum of solutions with specific charge and mass properties

Stable solutions without magnetic field nodes are identified

The moduli space exhibits fractal structure near zero cosmological constant

Abstract

A continuum of monopole, dyon and black hole solutions exist in the Einstein-Yang-Mills theory in asymptotically anti-de Sitter space. Their structure is studied in detail. The solutions are classified by non-Abelian electric and magnetic charges and the ADM mass. The stability of the solutions which have no node in non-Abelian magnetic fields is established. There exist critical spacetime solutions which terminate at a finite radius, and have universal behavior. The moduli space of the solutions exhibits a fractal structure as the cosmological constant approaches zero.