An instability of the Reissner-Nordstrom solution and new hairy black holes in d=5 dimensions

The d=5 Reissner-Nordstrom black hole becomes unstable when considered as a solution of Einstein--Yang-Mills--Chern-Simons theory. The existence of a marginally stable mode gives rise to a new branch of black holes with non-Abelian magnetic fields outside the horizon. These solutions carry a nonzero electric charge and have finite mass. We argue that these features manifest themselves both for Minkowski and (Anti-)de Sitter asymptotics. The properties of solutions in a de Sitter background are new to the present work and are emphasised. All solutions constructed have finite mass by virtue of the presence of the Chern-Simons term, which in d=5 plays the role of a higher order term scaling appropriately for this purpose.