On the global existence of spherically symmetric hairy black holes and solitons in anti-de Sitter Einstein-Yang-Mills theories with compact semisimple gauge groups

TL;DR

This paper proves the existence of spherically symmetric black hole and soliton solutions in anti-de Sitter Einstein-Yang-Mills theories with general semisimple gauge groups, extending previous results and highlighting differences from asymptotically flat cases.

Contribution

It generalizes existence results for black holes and solitons to broader gauge groups in adS space, contrasting with the asymptotically flat case and identifying stable solutions.

Findings

Solutions are less constrained at infinity for negative cosmological constant.

Existence of global solutions near trivial solutions and as |a| ightarrowaaa

Non-trivial solutions with gauge functions having no zeroes identified.

Abstract

We investigate the existence of black hole and soliton solutions to four dimensional, anti-de Sitter (adS), Einstein-Yang-Mills theories with general semisimple connected and simply connected gauge groups, concentrating on the so-called "regular" case. We here generalise results for the asymptotically flat case, and compare our system with similar results from the well-researched adS $\mathfrak{su}(N)$ system. We find the analysis differs from the asymptotically flat case in some important ways: the biggest difference is that for $\Lambda<0$, solutions are much less constrained as $r\rightarrow\infty$, making it possible to prove the existence of global solutions to the field equations in some neighbourhood of existing trivial solutions, and in the limit of $|\Lambda|\rightarrow\infty$. In particular, we can identify non-trivial solutions where the gauge field functions have no zeroes, which in the $\mathfrak{su}(N)$ case proved important to stability.