No nonminimally coupled massless scalar hair for spherically symmetric neutral black holes

TL;DR

This paper proves that spherically symmetric neutral black holes cannot have static nonminimally coupled massless scalar hair, using causality constraints on the energy-momentum tensor near the horizon.

Contribution

It offers a concise proof establishing the no-hair theorem for nonminimally coupled massless scalar fields around neutral black holes.

Findings

No static nonminimally coupled massless scalar hair for such black holes

Causality restrictions near the horizon are key to the proof

Supports the uniqueness of black hole solutions without scalar hair

Abstract

We provide a remarkably compact proof that spherically symmetric neutral black holes cannot support static nonminimally coupled massless scalar fields. The theorem is based on causality restrictions imposed on the energy-momentum tensor of the fields near the regular black-hole horizon.