Black holes have no short hair

TL;DR

This paper proposes a universal lower bound on the size of non-trivial matter field structures around black holes, suggesting that black holes cannot have 'short hair' and challenging the traditional no hair conjecture.

Contribution

It introduces the no short hair conjecture, asserting that non-trivial matter fields around black holes extend beyond 1.5 times the horizon radius, applicable across all theories with black hole hair.

Findings

Non-trivial matter fields extend beyond 1.5 times the horizon radius.

The no short hair conjecture is proposed as a universal principle.

Challenges the traditional no hair conjecture by providing a lower bound.

Abstract

We show that in all theories in which black hole hair has been discovered, the region with non-trivial structure of the non-linear matter fields must extend beyond 3/2 the horizon radius, independently of all other parameters present in the theory. We argue that this is a universal lower bound that applies in every theory where hair is present. This {\it no short hair conjecture} is then put forward as a more modest alternative to the original {\it no hair conjecture}, the validity of which now seems doubtful.