In a theory of quantum gravity, states can be represented as wavefunctionals
that assign an amplitude to a given configuration of matter fields and the metric on a spatial
slice. These wavefunctionals must obey a set of constraints as a consequence of the diffeomor-
phism invariance of the theory, the most important of which is known as the Wheeler-DeWitt
equation. We study these constraints perturbatively by expanding them to leading nontrivial
order in Newton’s constant about a background AdS spacetime. We show that, even within
perturbation theory, any wavefunctional that solves these constraints must have specific cor-
relations between a component of the metric at infinity and energetic excitations of matter
fields or transverse-traceless gravitons. These correlations disallow strictly localized excita-
tions.