Reissner–Nordström black holes with non-Abelian hair

We consider d⩾4 Einstein–(extended-)Yang–Mills theory, where the gauge sector is augmented by higher order terms. Linearising the (extended) Yang–Mills equations on the background of the electric Reissner–Nordström (RN) black hole, we show the existence of normalisable zero modes, dubbed non-Abelian magnetic stationary clouds. The non-linear realisation of these clouds bifurcates the RN family into a branch of static, spherically symmetric, electrically charged and asymptotically flat black holes with non-Abelian hair. Generically, the hairy black holes are thermodynamically preferred over the RN solution, which, in this model, becomes unstable against the formation of non-Abelian hair, for sufficiently large values of the electric charge.