Dyonic black holes in $\mathfrak{su}(\infty)$ anti-de Sitter Einstein–Yang–Mills theory, characterised by an infinite set of global charges

Abstract

We present solutions to classical field equations for purely magnetic su(∞) 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.The study of black hole hair is long and storied. The tale begins with the first "No-Hair" uniqueness theorems of Hawking and Israel [1][2][3], which concluded that static black holes were extremely simple objects and were characterised by 2 parameters: their Arno-Dewitt-Misner (ADM) mass M , and their electric charge e. A few decades later, infinite families of