How different are shadows of compact objects with and without horizons?

Abstract

In this work, we theoretically assume that a compact object (CO) has a dark surface such that this simplified CO has no emissions and no reflections. Considering that the radius of the surface can be located inside or outside the photon region, which is closely related to the shadow curve, we investigate whether a CO without an event horizon can produce shadow structures similar to those of black holes and compare the shadows of COs with and without horizons. In particular, by introducing the (possible) observational photon region, we analytically construct an exact correspondence between the shadow curves and the impact parameters of photons; we find that there are indeed several differences between the shadows of COs without horizons and those of black holes. More precisely, we find that the shadow curve is still determined by the photon region when the radius of the surface is small enough to retain a whole photon region outside the shell. When only part of the photon region remains, the shadow curve is partially determined by the photon region, and the remaining portion of the shadow curve is partly controlled by the impact parameters of photons that have a turning point on the surface. When there is no photon region outside the surface, the shadow curve is totally controlled by the impact parameters of photons, which have a turning point on the surface.