  In this note, we describe a holographic CFT construction of states dual to
scalar perturbations of the maximally extended three-dimensional
AdS-Schwarzschild black hole. The states are constructed by adding sources for
a scalar operator to the path integral that constructs the thermofield double
state. For a scalar field of arbitrary mass, we provide the general map between
sources and scalar field perturbations at linear order. With this, we
investigate to what extent it is possible using this construction to produce
perturbations localized to one side of the black hole horizon. Our results
suggest that it is possible to produce arbitrarily localized perturbations (and
thus, plausibly, general linear perturbations to the black hole initial data
slice), but that the amplitude of the perturbation must be taken small as the
perturbation becomes more localized in order that the sources do not diverge,
as found for the pure AdS case considered in arXiv:1709.10101.
