Charged SU(N) Einstein-Yang-Mills Black Holes

TL;DR

This paper explores static, spherically symmetric black hole solutions in SU(N) Einstein-Yang-Mills theory, classifying charged solutions and providing numerical examples for SU(5).

Contribution

It classifies charged black hole solutions in SU(N) EYM theory and presents numerical solutions for the SU(5) case.

Findings

Charged solutions involve non-abelian subalgebras and the Cartan subalgebra.

Numerical solutions are provided for SU(5).

Solutions include neutral and charged gauge field components.

Abstract

We consider asymptotically flat static spherically symmetric black hole solutions in SU(N) Einstein-Yang-Mills theory. Embedding the N-dimensional representation of $su(2)$ in $su(N)$, the purely magnetic gauge field ansatz contains $N-1$ functions. When one or more of these gauge field functions are identically zero, magnetically charged EYM black hole solutions emerge, consisting of a neutral and a charged gauge field part, based on non-abelian subalgebras and the Cartan subalgebra of $su(N)$, respectively. We classify these charged black hole solutions in general and present numerical solutions for SU(5) EYM theory.