  We undertake the task of studying the non-linear dynamics of quantum gravity
motivated alternatives to black holes that in the classical limit appear as
ultra-compact shells of matter. We develop a formalism that should be amenable
to numerical solution in generic situations. For a concrete model we focus on
the spherically symmetric AdS black bubble -- a shell of matter at the Buchdahl
radius separating a Schwarzschild exterior from an AdS interior. We construct a
numerical code to study the radial dynamics of and accretion onto AdS black
bubbles, with exterior matter provided by scalar fields. In doing so we develop
numerical methods that could be extended to future studies beyond spherical
symmetry. Regarding AdS black bubbles in particular, we find that the original
prescription for the internal matter fluxes needed to stabilize the black
bubble is inadequate in dynamical settings, and we propose a two parameter
generalization of the flux model to fix this. To allow for more efficient
surveys of parameter space, we develop a simpler numerical model adapted to
spherically symmetric bubble dynamics. We identify regions of parameter space
that do allow for stable black bubbles, and moreover allow control to a desired
end-state after an accretion episode. Based on these results, and evolution of
scalar fields on black bubble backgrounds, we speculate on some observational
consequences if what are currently presumed to be black holes in the universe
were actually black bubbles.
