How short can the hair of a black hole be?

TL;DR

This paper proposes a universal lower bound on the size of non-trivial matter field regions around black holes, suggesting that black hole hair cannot be arbitrarily short, challenging previous assumptions.

Contribution

It introduces the no short hair conjecture, asserting a universal minimum extent of black hole hair beyond the horizon radius across all theories.

Findings

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

The no short hair conjecture applies universally to all theories with black hole hair.

Challenges the previous no hair conjecture by proposing a minimal hair length.

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 now debunked {\it no hair conjecture}.