Shadows of spherically symmetric black holes and naked singularities

We compare shadows cast by Schwarzschild black holes with those produced by two classes of naked singularities that result from gravitational collapse of spherically symmetric matter. The latter models consist of an interior naked singularity spacetime restricted to radii r Rb, matched to Schwarzschild spacetime outside the boundary radius Rb. While a black hole always has a photon sphere and always casts a shadow, we find that the naked singularity models have photon spheres only if a certain parameter M₀ that characterizes these models satisfies M₀ 2/3, or equivalently, if Rb 3M, where M is the total mass of the object. Such models do produce shadows. However, models with M₀3M) have no photon sphere and do not produce a shadow. Instead, they produce an interesting `full-moon' image. These results imply that the presence of a shadow does not by itself prove that a compact object is necessarily a black hole. The object could be a naked singularity with M₀ 2/3, and we will need other observational clues to distinguish the two possibilities. On the other hand, the presence of a full-moon image would certainly rule out a black hole and might suggest a naked singularity with M₀<2/3. It would be worthwhile to generalize the present study, which is restricted to spherically symmetric models, to rotating black holes and naked singularities.