  We define a metric operator in the 1/2-BPS sector of the D1-D5 CFT, the
eigenstates of which have a good semi-classical supergravity dual; the
non-eigenstates cannot be mapped to semi-classical gravity duals. We also
analyse how the data defining a CFT state manifests itself in the gravity side,
and show that it is arranged into a set of multipoles. Interestingly, we find
that quantum mechanical interference in the CFT can have observable
manifestations in the semi-classical gravity dual. We also point out that the
multipoles associated to the normal statistical ensemble fluctuate wildly,
indicating that the mixed thermal state should not be associated to a
semi-classical geometry.
