Characterize islands of stability in the nonlinear instability of global AdS

Ascertain the size and structure of the islands of stability in the nonlinear evolution of perturbations in global Anti-de Sitter spacetime, as a function of the properties of the initial data, with particular emphasis on the limit of arbitrarily small total energy.

Background

Perturbations of global AdS exhibit the weak turbulent mechanism that generically leads to black hole formation, but there also exist families of initial data ("islands of stability") that do not collapse.

Understanding how large these islands are, and how their measure and structure depend on features of the initial data (e.g., mode content, symmetry, angular momentum), is crucial to a complete picture of the AdS nonlinear dynamics.

The paper notes that this remains an open problem, especially in the regime of very small energies where perturbations are weak.