  It has been suggested by A. Sen that the entropy of two-charge supersymmetric
bound states in string theory should be accounted for by adding the entropy of
source-free horizonless supergravity solutions to the entropy associated with
the horizons of small black holes. This would imply that the entropy arises
differently depending on the duality frame: in the D1-D5 frame one would count
source-free horizonless solutions, while in the NS1-P frame one would compute
the area of a horizon. This might lead to the belief that the microstates are
described by fuzzball solutions in the D1-D5 duality frame but by a black hole
with a horizon in the latter. We argue that this is not the case, and that the
microstates are fuzzballs in all duality frames. We observe that the scaling
argument used by Sen fails to account for the entropy in the D1-P and other
duality frames. We also note that the traditional extremal black hole solution
is not a complete string background, since finite-action paths connect the
exterior near-horizon extremal throat to the region inside the horizon,
including the singularity. The singularity of the traditional black hole
solution does not give a valid boundary condition for a fundamental string;
correcting this condition by resolving the singularity modifies the black hole
to a fuzzball with no horizon. We argue that for questions of counting states,
the traditional black hole solution should be understood through its Euclidean
continuation as a saddle point, and that the Lorentzian states being counted
are fuzzballs in all duality frames.
