  One version of the membrane paradigm states that as far as outside observers
are concerned, black holes can be replaced by a dissipative membrane with
simple physical properties located at the stretched horizon. We demonstrate
that such a membrane paradigm is incomplete in several aspects. We argue that
it generically fails to capture the massive quasinormal modes, unless we
replace the stretched horizon by the exact event horizon, and illustrate this
with a scalar field in a BTZ black hole background. We also consider as a
concrete example linearized metric perturbations of a five-dimensional
AdS-Schwarzschild black brane and show that a spurious excitation appears in
the long-wavelength response that is only removed from the spectrum when the
membrane paradigm is replaced by ingoing boundary conditions at the event
horizon. We interpret this excitation in terms of an additional Goldstone boson
that appears due to symmetry breaking by the classical solution ending on the
stretched horizon rather than the event horizon.
