Black hole hair: twenty--five years after

TL;DR

This paper reviews the concept of black hole hair, discusses recent solutions with gauge or Skyrme field hair, and presents new theorems supporting a no scalar-hair conjecture in general relativity.

Contribution

It introduces a no scalar-hair conjecture and provides new theorems that nearly prove it by excluding scalar field hair in most cases.

Findings

Existence of stable solutions with gauge or Skyrme field hair.

New theorems nearly establish the no scalar-hair conjecture.

Scalar hair is ruled out for most parameter ranges in spherical black holes.

Abstract

Originally regarded as forbidden, black hole ``hair'' are fields associated with a stationary black hole apart from the gravitational and electromagnetic ones. Several stable stationary black hole solutions with gauge or Skyrme field hair are known today within general relativity. We formulate here a ``no scalar--hair'' conjecture, and adduce some new theorems that almost establish it by ruling out - for all but a small parameter range - scalar field hair of spherical black holes in general relativity, whether the field be self--interacting, coupled to an Abelian gauge field, or nonminimally coupled to gravity.