  We address the question of the uniqueness of the Schwarzschild black hole by
considering the following question: How many meaningful solutions of the
Einstein equations exist that agree with the Schwarzschild solution (with a
fixed mass m) everywhere except maybe on a codimension one hypersurface? The
perhaps surprising answer is that the solution is unique (and uniquely the
Schwarzschild solution everywhere in spacetime) *unless* the hypersurface is
the event horizon of the Schwarzschild black hole, in which case there are
actually an infinite number of distinct solutions. We explain this result and
comment on some of the possible implications for black hole physics.
