  Most quantum states have wavefunctions that are widely spread over the
accessible Hilbert space and hence do not have a good description in terms of a
single classical geometry. In order to understand when geometric descriptions
are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of
asymptotically AdS_5 x S^5 universes. In this sector we devise a
"coarse-grained metric operator" whose eigenstates are well described by a
single spacetime topology and geometry. We show that such half-BPS universes
have a non-vanishing entropy if and only if the metric is singular, and that
the entropy arises from coarse-graining the geometry. Finally, we use our
entropy formula to find the most entropic spacetimes with fixed asymptotic
moments beyond the global charges.
