  Dirichlet walls -- timelike boundaries at finite distance from the bulk on
which the induced metric is held fixed -- have been used to model AdS
spacetimes with a finite cutoff. In the context of gauge/gravity duality, such
models are often described as dual to some novel UV-cufoff version of a
corresponding CFT that maintains local Lorentz invariance. We study linearized
gravity in the presence of such a wall and find it to differ significantly from
the seemingly-analogous case of Dirichlet boundary conditions for fields of
spins zero and one. In particular, using the Kodama-Ishibashi formalism, the
boundary condition that must be imposed on scalar-sector master field with
harmonic time dependence depends explicitly on their frequency. That this
feature first arises for spin-2 appears to be related to the second-order
nature of the equations of motion. It gives rise to a number of novel
instabilities, though both global and planar Anti-de Sitter remain (linearly)
stable in the presence of large-radius Dirichlet cutoffs. The instabilities
arise on the outside of spherical Dirichlet walls, and also inside sufficiently
large such spherical walls in de Sitter space. We analyze both inside and
outside of flat and spherical walls in Minkowski, de Sitter, and anti-de Sitter
space, as well as in certain black hole spacetimes and find stability for cases
not mentioned above. In particular, we find no linear instabilities in the
presence of flat walls. We also find evidence supporting the conjecture that
neutral black holes are repelled by Dirichlet walls.
