  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.
