Phase Transition to a Hairy Black Hole in Asymptotically Flat Spacetime

Abstract

We discuss a phase transition of a Reissner-Nordstr\"om black hole to a hairy black hole in asymptotically flat spacetime. The hair is due to a massive charged scalar field. The no-hair theorem is evaded thanks to a derivative coupling of the scalar field to the Einstein tensor. The resulting hairy configuration is spherically symmetric. We solve the equations analytically near the transition temperature and show that the hair is concentrated near the horizon decaying exponentially away from it.