# Stable furry black holes in $\mathfrak{su}(\infty)$ anti-de Sitter Einstein-Yang-Mills theory, characterised by an infinitude of global charges

## TL;DR

This paper constructs stable, purely magnetic $ ext{SU}( ext{infinity})$ Einstein-Yang-Mills solutions in Anti-de Sitter space, characterized by infinite global charges, challenging traditional no-hair conjectures.

## Contribution

It introduces a new class of stable, infinite-charge black hole solutions in $ ext{SU}( ext{infinity})$ Einstein-Yang-Mills theory within Anti-de Sitter space, expanding understanding of gauge field configurations.

## Key findings

- Solutions are stable under linear perturbations.
- Solutions are characterized by an infinite set of gauge-invariant charges.
- Revises the no-hair conjecture to include these solutions.

## Abstract

We present solutions to classical field equations for purely magnetic $\mathfrak{su}(\infty)$ Einstein-Yang-Mills theory in asymptotically Anti-de Sitter space. These solutions are found to be stable under linear, time-dependent perturbations. Recent work has also shown that these solutions may in general be uniquely characterized by a countably infinite set of asymptotically measured, gauge-invariant charges. In light of this discovery, we revisit Bizon's `modified No-Hair conjecture', and suggest a new version that accommodates these solutions.