  We investigate the microscopic origin of black hole entropy, in particular
the gap between the maximum entropy of ordinary matter and that of black holes.
Using curved space, we construct configurations with entropy greater than their
area in Planck units. These configurations have pathological properties and we
refer to them as monsters. When monsters are excluded we recover the entropy
bound on ordinary matter $S < A^{3/4}$. This bound implies that essentially all
of the microstates of a semiclassical black hole are associated with the growth
of a slightly smaller black hole which absorbs some additional energy. Our
results suggest that the area entropy of black holes is the logarithm of the
number of distinct ways in which one can form the black hole from ordinary
matter and smaller black holes, but only after the exclusion of monster states.
