Unwinding of strings thrown into a fuzzball

The traditional black hole has a horizon, with a singularity inside the horizon. But actual microstates of black holes are ‘fuzzballs’, with no horizon and a complex internal structure. We take the simplest hole in string theory — the extremal 2-charge D1D5 hole — and study a simple effect that is a consequence of this internal structure of the fuzzball. Suppose we have a NS1 string wrapping the compact circle of the fuzzball solution. In the traditional black hole solution this circle is directly tensored with the remaining directions, and does not shrink to zero size. Thus a part of the string can fall behind the horizon, but not ‘unwind’. In the fuzzball geometry, this circle makes a nontrivial geometric structure — the KK monople — by mixing with the other directions, and thus shrinks to zero at the core of the monopole. Thus the string can ‘unwind’ in the fuzzball geometry, and the winding charge is then manifested by a nontrivial field strength living on the microstate solution. We compute this field strength for a generic microstate, and comment briefly on the physics suggested by the unwinding process.