Toward the New Gravitational Noncommutative Mechanics and Statistical   Mechanics of Quantum Black Holes
  This is a short account of our work on the statistical mechanics of `cold' quantum black holes in the constituent model of a black hole$^{3,4,6}$. A quantum Schwarzschild black hole consists of gravitational atoms of Planckian mass scale$^{3,4,6}$. The gapless collective excitations of a bound state of N gravitational atoms dominate the thermodynamics of a cold quantum black hole. It turns out that it is only in the limit of large $N$, with the observable mean values of the gravitational mass-energy kept fixed, that we recover the Bekenstein thermodynamics$^1$ of spin-zero black holes. This is also the limit of the Boltzmann statistics. 
P. O. Mazur