We revisit the box Minkowski model [Phys. Rev. Lett. 109, 221101 (2012)] and
provide a strong argument that, subject to the Dirichlet boundary condition, it
is unstable toward black hole formation for arbitrarily small generic
perturbations. Using weakly nonlinear perturbation theory, we derive the
resonant system, which compared to systems with the anti-de Sitter asymptotics,
has extra resonant terms, and study its properties, including conserved
quantities. We find that the generic solution of the resonant system becomes
singular in finite time. Surprisingly, the additional resonant interactions do
not significantly affect the singular evolution. Furthermore, we find that the
interaction coefficients take a relatively simple form, making this a
particularly attractive toy model of turbulent gravitational instability.
