black holes

Monthly Notices of the Royal Astronomical Society

We compare shadows cast by Schwarzschild black holes with those produced by\ntwo classes of naked singularities that result from gravitational collapse of\nspherically symmetric matter. The latter models consist of an interior naked\nsingularity spacetime restricted to radii $r\\leq R_b$, matched to Schwarzschild\nspacetime outside the boundary radius $R_b$. While a black hole always has a\nphoton sphere and always casts a shadow, we find that the naked singularity\nmodels have photon spheres only if a certain parameter $M_0$ that characterizes\nthese models satisfies $M_0\\geq 2/3$, or equivalently, if $R_b\\leq 3M$, where\n$M$ is the total mass of the object. Such models do produce shadows. However,\nmodels with $M_0&lt;2/3$ (or $R_b&gt;3M$) have no photon sphere and do not produce a\nshadow. Instead, they produce an interesting `full-moon' image. These results\nimply that the presence of a shadow does not by itself prove that a compact\nobject is necessarily a black hole. The object could be a naked singularity\nwith $M_0\\geq 2/3$, and we will need other observational clues to distinguish\nthe two possibilities. On the other hand, the presence of a full-moon image\nwould certainly rule out a black hole and might suggest a naked singularity\nwith $M_0&lt;2/3$. It would be worthwhile to generalize the present study, which\nis restricted to spherically symmetric models, to rotating black holes and\nnaked singularities.\n

Shadows of spherically symmetric black holes and naked singularities