Phase Transition to a Hairy Black Hole in Asymptotically Flat Spacetime

TL;DR

This paper investigates a phase transition from a Reissner-Nordström black hole to a hairy black hole in flat spacetime, facilitated by a derivative coupling of a charged scalar field, with analytical solutions near the transition.

Contribution

It demonstrates a novel mechanism to evade the no-hair theorem via derivative coupling, leading to a new class of hairy black hole solutions in asymptotically flat spacetime.

Findings

Hair is concentrated near the horizon and decays exponentially outward.

Analytical solutions are obtained near the transition temperature.

The no-hair theorem is evaded through derivative coupling to the Einstein tensor.

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.