  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.
