Fastest way to circle a black hole

Black-hole spacetimes with a photonsphere, a hypersurface on which massless particles can orbit the black hole on circular null geodesics, are studied. We prove that among all possible trajectories (both geodesic and nongeodesic) which circle the central black hole, the null circular geodesic is characterized by the shortest possible orbital period as measured by asymptotic observers. Thus, null circular geodesics provide the fastest way to circle black holes. In addition, we conjecture the existence of a universal lower bound for orbital periods around compact objects (as measured by flat-space asymptotic observers): T-infinity >= 4 pi M, where M is the mass of the central object. This bound is saturated by the null circular geodesic of the maximally rotating Kerr black hole.