Lower bound of black hole hair in pure Lovelock theory of gravity

TL;DR

This paper investigates the extent of black hole hair in pure Lovelock gravity, demonstrating that such hair always extends at least up to the photon sphere, regardless of dimension or Lovelock order.

Contribution

It provides the first analysis of the 'no short hair' conjecture within pure Lovelock gravity, establishing a universal lower bound for black hole hair extension.

Findings

Hair extends beyond the photon sphere in pure Lovelock black holes.

The extension of hair is independent of dimensionality and Lovelock order.

The 'no short hair' conjecture holds in pure Lovelock gravity.

Abstract

As an alternative to the "no hair conjecture," the "no short hair conjecture" for hairy black holes was established earlier. This theorem stipulates that hair must be present above 3/2 of the event horizon radius for a hairy black hole. It is assumed that the nonlinear behavior of the matter field plays a key role in the presence of such hair. Subsequently, it was established that the hair must extend beyond the photon sphere of the corresponding black hole. We have investigated the validity of the "no short hair conjecture" in pure Lovelock gravity. Our analysis has shown that irrespective of dimensionality and Lovelock order, the hair of a static, spherically symmetric black hole extends at least up to the photon sphere.