  One of the most remarkable predictions of the general theory of relativity is
the existence of black-hole "photonspheres", compact null hypersurfaces on
which massless particles can orbit the central black hole. We prove that every
spherically-symmetric asymptotically flat black-hole spacetime is characterized
by a photonsphere whose radius is bounded from above by $r_{\gamma} \leq 3M$,
where $M$ is the total ADM mass of the black-hole spacetime. It is shown that
hairy black-hole configurations conform to this upper bound. In particular, the
null circular geodesic of the (bald) Schwarzschild black-hole spacetime
saturates the bound.
