Lower bound on the radii of black-hole shadows

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.