Black hole mimickers: regular versus singular behavior
  Black hole mimickers are possible alternatives to black holes, they would look observationally almost like black holes but would have no horizon. The properties in the near-horizon region where gravity is strong can be quite different for both type of objects, but at infinity it could be difficult to discern black holes from their mimickers. To disentangle this possible confusion, we examine the near-horizon properties, and their connection with far away properties, of some candidates to black mimickers. We study spherically symmetric uncharged or charged but non-extremal objects, as well as spherically symmetric charged extremal objects. Within the uncharged or charged but non-extremal black hole mimickers, we study non-extremal $\epsilon$-wormholes on the threshold of the formation of an event horizon, of which a subclass are called black foils, and gravastars. Within the charged extremal black hole mimickers we study extremal $\epsilon$-wormholes on the threshold of the formation of an event horizon, quasi-black holes, and wormholes on the basis of quasi-black holes from Bonnor stars. We elucidate, whether or not the objects belonging to these two classes remain regular in the near-horizon limit. The requirement of full regularity, i.e., finite curvature and absence of naked behavior, up to an arbitrary neighborhood of the gravitational radius of the object enables one to rule out potential mimickers in most of the cases. A list ranking the best mimickers up to the worse is given. Since, in observational astrophysics it is difficult to find extremal configurations (the best mimickers in the ranking), whereas non-extremal configurations are really bad mimickers, the task of distinguishing black holes from their mimickers seems to be less difficult than one could think of. 
Jos\'e P. S. Lemos, Oleg B. Zaslavskii