Resonant dynamics and the instability of the box Minkowski model

Abstract

We revisit the box Minkowski model [M. Maliborski, Instability of Flat Space Enclosed in a Cavity, 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.