Reissner-Nordstr\"om black holes with non-Abelian hair

TL;DR

This paper demonstrates the existence of non-Abelian magnetic clouds around Reissner-Nordström black holes in extended Yang-Mills theory, leading to new hairy black hole solutions that are thermodynamically favored over RN black holes.

Contribution

It introduces non-Abelian hair to Reissner-Nordström black holes via higher order Yang-Mills terms, revealing new stable black hole solutions with non-Abelian fields.

Findings

Existence of normalizable zero modes (magnetic clouds) around RN black holes.

Bifurcation of RN solutions into non-Abelian hairy black holes.

Hairy black holes are thermodynamically preferred at high electric charge.

Abstract

We consider $d\geqslant 4$ Einstein--(extended-)Yang-Mills theory, where the gauge sector is augmented by higher order terms. Linearizing the (extended) Yang-Mills equations on the background of the electric Reissner-Nordstr\"om (RN) black hole, we show the existence of normalizable zero modes, dubbed non-Abelian magnetic stationary clouds. The non-linear realization 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.