  Under the premises that physics is unitary and black hole evaporation is
complete (no remnants, no topology change), there must exist a one-to-one
correspondence between states on future null and timelike infinity and on any
earlier spacelike Cauchy surface (e.g., slices preceding the formation of the
hole). We show that these requirements exclude a large set of semiclassical
spacetime configurations from the Hilbert space of quantum gravity. In
particular, the highest entropy configurations, which account for almost all of
the volume of semiclassical phase space, would not have quantum counterparts,
i.e. would not correspond to allowed states in a quantum theory of gravity.
