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

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 $\mathrm{su}(2)$ in $\mathrm{su}(4),$ 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 behavior 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.