Shadow of a dressed black hole and determination of spin and viewing angle

Shadows of black holes surrounded by an optically thin emitting medium have been extensively discussed in the literature. The Hioki-Maeda algorithm is a simple recipe to characterize the shape of these shadows and determine the parameters of the system. Here, we extend their idea to the case of a dressed black hole, namely a black hole surrounded by a geometrically thin and optically thick accretion disk. While the boundary of the shadow of black holes surrounded by an optically thin emitting medium corresponds to the apparent photon capture sphere, that of dressed black holes corresponds to the apparent image of the innermost stable circular orbit (ISCO). Even in this case, we can characterize the shape of the shadow and infer the black hole spin and viewing angle. The shape and the size of the shadow of a dressed black hole are strongly affected by the black hole spin and inclination angle. Despite that, it seems that we cannot extract any additional information from it. Here, we study the possibility of testing the Kerr metric. Even with the full knowledge of the boundary of the shadow, those of Kerr and non-Kerr black holes are very similar and it is eventually very difficult to distinguish the two cases.