AdS nonlinear instability: moving beyond spherical symmetry

Abstract

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 [2]. In contrast with [2], 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 [2]. Moreover, if the seed has two normal modes, more than one resonance can be generated at third order, unlike the spherical collapse of [2]. 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.

Gravitational geons in asymptotically anti-de Sitter spacetimes

“…We recover in the low amplitude limit the perturbative results up to fifth order, and give predictions about coefficients appearing at successive orders. Last but not least, we provide numerical evidence that radially excited geons, whose existence was debated in [57][58][59], do exist in AdS spacetimes. We compute them numerically and finally show their existence curves in phase space.…”

Black resonators and geons in AdS 5

“…(See also [23] for a perturbative study.) Recently, the generalization beyond preserving the spherical symmetry has also been considered [38][39][40][41][42]. It would be favorable to take into account the effect of rotations also from our perspective.…”

AdS nonlinear instability: breaking spherical and axial symmetries

“…However, in [2], only a certain class of perturbations was considered, for which the perturbative analysis considerably simplifies. In this manuscript we present details of the systematic computational formalism and an exhaustive and complementary analysis of physical properties of the geons and gravitational AdS instability that were absent in our companion Letter [3]. In particular, we find that, unlike in spherical symmetry, a (single) gravitational normal mode of AdS can be backreacted to generate a nonlinear solution only in very exceptional circumstances.…”

“…In short, one can consider standard perturbation theory whereby the expansion parameter is the amplitude ε of a linear seed, and this seed is a linear combination of normal modes of global AdS which have a quantized spectrum of frequencies. Extending the perturbative expansion to third order, one generically finds secular term(s) of the form t ε 3 . Such a linear growth in time of the amplitude at third order invalidates the perturbation scheme for timescales t ≥ ε −2 .…”