A Kolmogorov-Zakharov Spectrum in AdS Gravitational Collapse

We study black hole formation during the gravitational collapse of a massless scalar field in asymptotically AdS_D spacetimes for D = 4, 5. We conclude that spherically symmetric gravitational collapse in asymptotically AdS spaces is turbulent and characterized by a Kolmogorov-Zakharov spectrum. Namely, we find that after an initial period of weakly nonlinear evolution, there is a regime where the power spectrum of the Ricci scalar evolves as k^{-s} with the wave number, k, and s ≈ 1.61 which is tantalizingly close to Kolmogorov’s 5/3.