Maxwell–Boltzmann type Hawking radiation

Twenty years ago, Rovelli proposed that the degeneracy of black hole (i.e. the exponential of the Bekenstein–Hawking entropy) is given by the number of ways the black hole horizon area can be expressed as a sum of unit areas. However, when counting the sum, one should treat the area quanta on the black hole horizon as distinguishable. This distinguishability of area quanta is noted in Rovelli’s paper. Building on this idea, we derive that the Hawking radiation spectrum is not given by Planck radiation spectrum (i.e. Bose–Einstein distribution) but given by Maxwell–Boltzmann distribution.