Lower bound on the radii of black-hole shadows

TL;DR

This paper establishes a theoretical lower bound on the size of black-hole shadows in spherically symmetric hairy black-hole spacetimes, showing that the shadow radius is at least 3√3/2 times the horizon radius, with the Schwarzschild case saturating this bound.

Contribution

It provides the first analytical lower bound on black-hole shadow radii in hairy black-hole spacetimes under the weak energy condition.

Findings

Shadow radius bound: r_sh/r_H ≥ 3√3/2

Schwarzschild shadow saturates the bound

Bound applies to spacetimes with matter fields satisfying the weak energy condition

Abstract

The non-linearly coupled Einstein-matter field equations predict the existence of shadows with well-defined boundaries around black holes. We prove that, in spherically symmetric hairy black-hole spacetimes whose matter fields satisfy the weak energy condition, the radii of these shadows are bounded from below by the dimensionless relation $r_{\text{sh}}/r_{\text{H}}\geq 3\sqrt{3}/2$, where $r_{\text{H}}$ is the horizon radius of the central hairy black hole. The characteristic shadow of the (bald) Schwarzschild black-hole spacetime saturates the analytically derived lower bound.