Sequences of globally regular and black hole solutions in SU(4) Einstein-Yang-Mills theory

TL;DR

This paper classifies and analyzes sequences of static spherically symmetric solutions, including black holes, in SU(4) Einstein-Yang-Mills theory, revealing their limiting behaviors, charge properties, and critical phenomena.

Contribution

It provides a comprehensive classification of solutions based on node numbers, explores their limiting solutions and charge characteristics, and compares SU(4) solutions with Einstein-Yang-Mills-dilaton counterparts.

Findings

Sequences of solutions are classified by node numbers and exhibit distinct limiting behaviors.

Limiting solutions of neutral sequences carry charge, while charged ones carry higher charge.

Multiple solution branches exist up to critical horizon radii, with detailed critical behavior analysis.

Abstract

SU(4) Einstein-Yang-Mills theory possesses sequences of static spherically symmetric globally regular and black hole solutions. Considering solutions with a purely magnetic gauge field, based on the 4-dimensional embedding of $su(2)$ in $su(4)$, these solutions are labelled by the node numbers $(n_1,n_2,n_3)$ of the three gauge field functions $u_1$, $u_2$ and $u_3$. We classify the various types of solutions in sequences and determine their limiting solutions. The limiting solutions of the sequences of neutral solutions carry charge, and the limiting solutions of the sequences of charged solutions carry higher charge. For sequences of black hole solutions with node structure $(n,j,n)$ and $(n,n,n)$, several distinct branches of solutions exist up to critical values of the horizon radius. We determine the critical behaviour for these sequences of solutions. We also consider SU(4) Einstein-Yang-Mills-dilaton theory and show that these sequences of solutions are analogous in most respects to the corresponding SU(4) Einstein-Yang-Mills sequences of solutions.