  Supersymmetric black holes are characterized by a large number of degenerate
ground states. We argue that these black holes, like other quantum mechanical
systems with such a degeneracy, are subject to a phenomenon which is called the
geometric or Berry's phase: under adiabatic variations of the background values
of the supergravity moduli, the quantum microstates of the black hole mix among
themselves. We present a simple example where this mixing is exactly
computable, that of small supersymmetric black holes in 5 dimensions. While in
practice it would be extremely difficult to measure Berry's phase for black
holes, it may be interesting to explore it further from a theoretical point of
view, as it provides us with a way to probe, and to some degree manipulate, the
quantum microstate of the black hole.
