Spherical polytropic balls cannot mimic black holes

Understand

The so-called black hole shadow is a dark region which is expected to appear in a fine image of optical observation of black holes.

• It is essentially an absorption cross section of black hole, and the boundary of shadow is determined by unstable circular orbits of photons (UCOP).
• If there exists a compact object possessing UCOP but no black hole horizon, it can provide us with the same shadow image with black holes, and a detection of shadow image cannot be a direct evidence of black hole existence.
• Then, this paper examine whether or not such compact objects can exist under some suitable conditions.