  The evolution of black holes in "confining boxes" is interesting for a number
of reasons, particularly because it mimics the global structure of Anti-de
Sitter geometries. These are non-globally hyperbolic space-times and the Cauchy
problem may only be well defined if the initial data is supplemented by
boundary conditions at the time-like conformal boundary. Here, we explore the
active role that boundary conditions play in the evolution of a bulk black hole
system, by imprisoning a black hole binary in a box with mirror-like boundary
conditions. We are able to follow the post-merger dynamics for up to two
reflections off the boundary of the gravitational radiation produced in the
merger. We estimate that about 15% of the radiation energy is absorbed by the
black hole per interaction, whereas transfer of angular momentum from the
radiation to the black hole is only observed in the first interaction. We
discuss the possible role of superradiant scattering for this result. Unlike
the studies with outgoing boundary conditions, both the Newman-Penrose scalars
\Psi_4 and \Psi_0 are non-trivial in our setup, and we show that the numerical
data verifies the expected relations between them.
