The fate for the interior content of a Black Hole from one-quarter entropy area-law

In this paper we continue investigations concerning the physical nature of the black hole entropy. In particular, in order to depict massless excitations (gravitons) leading to the one-quarter entropy area law, we use a mechanical statistical approach. As a first result, we obtain that, starting with a radiation field, we cannot exactly obtain the one-quarter factor in entropy area law. In the aforementioned framework, the correct black hole entropy is obtained only in the case where the internal temperature T i , proportional to the Bekenstein-Hawking one, is such that T i → 0 . As a consequence, according to other similar proposals in the literature, only a kind of Bose–Einstein condensate (BEC) can exactly support the black hole entropy. • Black entropy area law is derived with statistical mechanic methods. • A gas of gravitons is adopted. • A BEC of gravitons generate the exacy black hole entropy.