  In Lorentzian AdS/CFT there exists a mapping between local bulk operators and
nonlocal CFT operators. In global AdS this mapping can be found through use of
bulk equations of motion and allows the nonlocal CFT operator to be expressed
as a local operator smeared over a range of positions and times. We argue that
such a construction is not possible if there are bulk normal modes with
exponentially small near boundary imprint. We show that the AdS-Schwarzschild
background is such a case, with the horizon introducing modes with angular
momentum much larger than frequency, causing them to be trapped by the
centrifugal barrier. More generally, we argue that any barrier in the radial
effective potential which prevents null geodesics from reaching the boundary
will lead to modes with vanishingly small near boundary imprint, thereby
obstructing the existence of a smearing function. While one may have thought
the bulk-boundary dictionary for low curvature regions, such as the exterior of
a black hole, should be as in empty AdS, our results demonstrate otherwise.
