A recent proposal by Dvali and Gómez states that black holes (BH) can be treated as if they consisted of a Bose-Einstein condensate (BEC) of gravitons. In this talk I will present a summary of the results obtained by digging deep into this theory. In [1609.01639] we extended Einstein-Hilbert action with a chemical potential-like term and analyzed its characteristics in detail. The expanded equations resemble a Gross-Pitaevskii equation describing a BEC trapped by the BH gravitational field. The solution for this set of equations implies the BEC vanishes outside the horizon, but is non-zero in the interior. Also provides hints for finding an exact non-trivial solution for a mean-field wave-function describing the BEC in the BH interior. With the latter solution, some relations suggested by Dvali and Gómez that involve the number of gravitons N and the BH characteristics, summarized in its Schwarzschild radius, are rederived. In our picture, these characteristic are parametrized by a single parameter: a dimensionless chemical potentia.