Schwarzschild Black Hole Quantum Statistics, Droplet Nucleation and DLCQ Matrix Theory

Abstract

Generalizing previous quantum gravity results for Schwarzschild black holes from 4 to D>4 spacetime dimensions yields an energy spectrum E_n = n^{1-1/(D-2)} sigma E_P, n=1,2,..., sigma = O(1). Assuming the degeneracies of these levels to be given by g^n, g>1, leads to a partition function which is the same as that of the primitive droplet nucleation model for 1st-order phase transitions in D-2 spatial dimensions. Exploiting the well-known properties of the so-called critical droplets of this model immediately leads to the Hawking temperature and the Bekenstein-Hawking entropy of Schwarzschild black holes. Thus, the "holographic principle" of 't Hooft and Susskind is naturally realised. The values of temperature and entropy appear closely related to the imaginary part of the partition function which describes metastable states. Finally some striking conceptual similarities ("correspondence point" etc.) between the droplet nucleation picture and the very recent approach to the quantum statistics of Schwarzschild black holes in the framework of the DLCQ Matrix theory are pointed out.