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arXiv · 1602.03890

AdS nonlinear instability: moving beyond spherical symmetry

Oscar J. C. Dias·Jorge E. Santos
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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.

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Oscar J. C. Dias, Jorge E. Santos. 2016-02-11. AdS nonlinear instability: moving beyond spherical symmetry. https://doi.org/10.1088/0264-9381%2F33%2F23%2F23lt01

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