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We define a metric operator in the 1/2-BPS sector of the D1-D5 CFT, theeigenstates of which have a good semi-classical supergravity dual; thenon-eigenstates cannot be mapped to semi-classical gravity duals. We alsoanalyse 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 findthat quantum mechanical interference in the CFT can have observablemanifestations in the semi-classical gravity dual. We also point out that themultipoles associated to the normal statistical ensemble fluctuate wildly,indicating that the mixed thermal state should not be associated to asemi-classical geometry.

On the existence of supergravity duals to D1--D5 CFT states