On Statistical Mechanics of Schwarzschild Black Hole

Quantum theory of geometry that has been developed recently in the framework of non-perturbative quantum gravity is used in an attempt to explain thermodynamics of Schwarzschild black hole on the basis of microscopical (quantum) description. We work with the formulation of thermodynamics in which black hole is enclosed by a spherical surface B and a macroscopic state of the system is speciied by two parameters: the area of the boundary surface and the quasilocal energy contained within. To derive thermodynamical properties of the system from its microscopics we use the statistical mechanical method of Gibbs. We nd that microscopic (quantum) states of our system are naturally described by states of quantum Chern-Simons theories deened by sets of points on B with spins attached. The level of the Chern-Simons theories turns out to be proportional to the horizon area of black hole. We nd that the statistical mechanical analysis is especially simple in two cases. When the entire interior of B is occupied by a black hole, we nd that the entropy contained within B, that is, the black hole entropy, is proportional to the horizon surface area. Surprisingly, we nd that in the case when the mass contained within B is zero, the entropy of the system is not zero. This entropy turns out to be proportional to the square root of the boundary surface area.