Indexed on: 11 Feb '16Published on: 11 Feb '16Published in: High Energy Physics - Theory
Anti-de Sitter (AdS) is conjectured to be nonlinear unstable to a weakly turbulent mechanism that develops a cascade towards high frequencies, leading to black hole formation [1,2]. We give evidence that the gravitational sector of perturbations behaves differently from the scalar one studied in . In contrast with , we find that not all gravitational normal modes of AdS can be nonlinearly extended into periodic horizonless smooth solutions of the Einstein equation. In particular, we show that even seeds with a single normal mode can develop secular resonances, unlike the spherically symmetric scalar field collapse studied in . Moreover, if the seed has two normal modes, more than one resonance can be generated at third order, unlike the spherical collapse of . We also show that weak turbulent perturbative theory predicts the existence of direct and inverse cascades, with the former dominating the latter for equal energy two-mode seeds.