  In the LLM bubbling geometries, we compute the entropies of black holes and
estimate their "horizon" sizes from the fuzzball conjecture, based on
coarse-graining on the gravity side. The differences of black hole microstates
cannot be seen by classical observations. Conversely, by counting the possible
deformations of the geometry which are not classically detectable, we can
calculate the entropy. We carry out this method on the black holes of the LLM
bubbling geometries, such as the superstar, and obtain the same result as was
derived by coarse-graining directly on the CFT (fermion) side. Second, by
application of this method, we can estimate the "horizon" sizes of those black
holes, based on the fuzzball conjecture. The Bekenstein-Hawking entropy
computed from this "horizon" agrees with that microscopic entropy above. This
result supports the fuzzball conjecture.
