  A solution to the black hole information problem requires propagation of
information from the interior of the black hole to the exterior. Such
propagation violates general relativity and could conceivably be accomplished
through "firewall" models. Based on the existence of similar firewalls at the
inner horizons of charged and rotating black holes, a model of a firewall was
recently constructed where the exterior spacetime reduces to that of the
Schwarzschild metric but with a dramatically different interior. We investigate
the radial and nonradial polar stability of these objects. We first study the
dynamics of the shell under spherically symmetric perturbations, and impose
constraints on the firewall model parameters by requiring a subluminal speed of
sound on the firewall. We show that the demands of stability and subluminality
impose significant constraints on the internal parameters of the firewall,
narrowing down the range of objects that could be used to create such a
structure.
