Black hole horizons must be veiled by photon spheres

Horizons and bound photon orbits are defining features of black holes that translate into key features of black hole images. We present a purely geometric proof that spherically symmetric, isolated objects with horizons in gravity theories with null-geodesic propagation of light must display bound photon orbits forming a photon sphere. Identifying the key elements of the proof, we articulate a simpler argument that carries over to more general situations with modified light propagation and implies the existence of equatorial spherical photon orbits in axisymmetric spacetimes with reflection symmetry. We conclude that the non-observation of photon rings with very-large-baseline interferometry would be a very strong indication against a horizon, irrespective of whether or not the image shows a central brightness depression.