  The discovery of a "weakly-turbulent" instability of anti-de Sitter spacetime
supports the idea that confined fluctuations eventually collapse to black holes
and suggests that similar phenomena might be possible in asymptotically-flat
spacetime, for example in the context of spherically symmetric oscillations of
stars or nonradial pulsations of ultracompact objects. Here we present a
detailed study of the evolution of the Einstein-Klein-Gordon system in a
cavity, with different types of deformations of the spectrum, including a mass
term for the scalar and Neumann conditions at the boundary. We provide
numerical evidence that gravitational collapse always occurs, at least for
amplitudes that are three orders of magnitude smaller than Choptuik's critical
value and corresponding to more than $10^5$ reflections before collapse. The
collapse time scales as the inverse square of the initial amplitude in the
small-amplitude limit. In addition, we find that fields with nonresonant
spectrum collapse earlier than in the fully-resonant case, a result that is at
odds with the current understanding of the process. Energy is transferred
through a direct cascade to high frequencies when the spectrum is resonant, but
we observe both direct- and inverse-cascade effects for nonresonant spectra.
Our results indicate that a fully-resonant spectrum might not be a crucial
ingredient of the conjectured turbulent instability and that other mechanisms
might be relevant. We discuss how a definitive answer to this problem is
essentially impossible within the present framework.
