Lower bound on the radii of black-hole photonspheres

TL;DR

This paper proves a conjecture that the radii of black-hole photonspheres are bounded below by 1.5 times the horizon radius for certain spherically symmetric hairy black holes with specific pressure conditions.

Contribution

It establishes the lower bound on photonsphere radii for a class of hairy black holes, confirming a recent conjecture in general relativity.

Findings

Validates the conjecture for specific black-hole configurations.

Provides a mathematical proof under monotonic pressure conditions.

Enhances understanding of photon orbits around black holes.

Abstract

The existence of closed null circular geodesics around black holes is one of the most intriguing predictions of general relativity. It has recently been conjectured that the radii of black-hole photonspheres are bounded from below by the simple relation $r_{\text{ph}}\geq {3\over2}r_{\text{H}}$, where $r_{\text{H}}$ is the radius of the outer black-hole horizon. We here prove the validity of this conjecture for spherically symmetric hairy black-hole configurations whose radial pressure function $P\equiv |r^3p|$ decreases monotonically.