Hairy Black Holes and Null Circular Geodesics

TL;DR

This paper investigates hairy black holes, proving that their nontrivial features extend beyond the photonsphere and conjecturing that at least half of the hair's mass resides above this region, supported by analytical and numerical evidence.

Contribution

It establishes that black hole hair extends beyond the photonsphere and proposes a mass distribution conjecture, supported by new analytical and numerical results.

Findings

Hair extends beyond the photonsphere.

At least 50% of hair's mass is above the photonsphere.

Numerical and analytical evidence supports the conjecture.

Abstract

Einstein-matter theories in which hairy black-hole configurations have been found are studied. We prove that the nontrivial behavior of the hair must extend beyond the null circular orbit (the photonsphere) of the corresponding spacetime. We further conjecture that the region above the photonsphere contains at least 50% of the total hair's mass. We support this conjecture with analytical and numerical results.