Possible connection between dark matter and supermassive black holes

Dark Matter (DM) is usually studied in connection with rotational curves in the outskirts of the galaxies. However, the role of DM might be different in the galactic bulges and centers where Supermassive Black Holes (SMBHs) dominate the gravitational interaction. Indeed, given the fact that DM is the dominant matter species in the Universe, it is natural to assume a close connection between DM and SMBHs. Here we probe into this possibility by constructing stable objects with fuzzy mass distributions based on standard DM profiles. These astrophysical objects come out in three types: a fuzzy droplet without horizon and fuzzy Black Holes (BHs) with one or two horizons. We emphasize that all objects are solutions of Einstein equations. Their effective potentials which govern the motion of a test body, can display a reasonable similarity to the effective potential of a Schwarzschild BH at the galactic center. Therefore, some of our solutions could, in principle, replace the standard BH-picture of the galactic center and, at the same time, have the advantage that they have been composed of the main matter ingredient of the Universe.