Toward the New Gravitational Noncommutative Mechanics and Statistical Mechanics of Quantum Black Holes

摘要

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$^{3,4,6}$. Aquantum Schwarzschild black hole consists of gravitational atoms of Planckianmass scale$^{3,4,6}$. The gapless collective excitations of a bound state of Ngravitational 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 observablemean values of the gravitational mass-energy kept fixed, that we recover theBekenstein thermodynamics$^1$ of spin-zero black holes. This is also the limitof the Boltzmann statistics.