Quantum Dust Black Holes A Statistical Mechanics Derivation of Black Holes Thermodynamics

By analysing the infinite-dimensional midisuperspace of spherically symmetric dust matter universes, and applying it to collapsing dust stars, one finds that the general quantum state is a bound state. This leads to a discrete spectrum. To an outside observer, the geometry is static if the initial radius of the collapsing star is smaller then the Schwarzschild radius. In that case the discrete spectrum implies Bekenstein area quantization: the area of the black hole is an integer multiple of the Planck area. Knowing the microscopic (quantum) states, we suggest a microscopic interpretation of the thermodynamics of black holes: by calculating the degeneracy of the quantum states forming a black hole, one gets the Bekenstein-Hawking entropy (the entropy is proportional to the surface area of the black hole). All other thermodynamical quantities can be derived by using the standard definitions. This work is supported by the NSF grant PHY 88-04561 and by a Fishbach Fellowship 1