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

TL;DR

This paper investigates whether compact objects without horizons can produce shadow structures similar to black holes, analyzing how the presence or absence of a photon region affects the shadow curves.

Contribution

It provides an analytical framework linking shadow curves to photon regions and impact parameters, highlighting differences between horizons and horizonless compact objects.

Findings

Shadow curves are influenced by the photon region when the surface radius is small.

Partial photon regions lead to mixed control of the shadow curve.

Without a photon region, the shadow is determined solely by photon impact parameters.

Abstract

In this work, we theoretically assume that a compact object (CO) can have a dark surface so that the CO is simplified to have no emissions and 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 if a CO without an event horizon could produce shadow structures similar to black holes and figure out how different of 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 with the impact parameters of photons and find that there are indeed several differences for shadows of COs without horizons and black holes. More precisely, We found 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 which has a turning point on the surface. When there's no photon region outside the surface, the shadow curve is totally controlled by the impact parameters of photons which has a turning point on the surface.