Shadows of spherically symmetric black holes and naked singularities

TL;DR

This paper compares the shadows of Schwarzschild black holes with those of naked singularities from spherical collapse, revealing conditions under which naked singularities can produce shadows or full-moon images, challenging the uniqueness of shadows as black hole indicators.

Contribution

It identifies specific parameter regimes where naked singularities can mimic black hole shadows or produce distinct full-moon images, expanding the understanding of observational signatures.

Findings

Black holes always cast shadows with photon spheres.

Naked singularities can produce shadows if a parameter M_0 ≥ 2/3.

Naked singularities with M_0 < 2/3 do not produce shadows, but show full-moon images.

Abstract

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 $r\leq R_b$, matched to Schwarzschild spacetime outside the boundary radius $R_b$. 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 $M_0$ that characterizes these models satisfies $M_0\geq 2/3$, or equivalently, if $R_b\leq 3M$, where $M$ is the total mass of the object. Such models do produce shadows. However, models with $M_0<2/3$ (or $R_b>3M$) 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 $M_0\geq 2/3$, 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 $M_0<2/3$. It would be worthwhile to generalize the present study, which is restricted to spherically symmetric models, to rotating black holes and naked singularities.