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What drives AdS unstable?

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arxiv 1403.5434 v2 pith:NITTBUSA submitted 2014-03-21 gr-qc hep-th

Maciej Maliborski , Andrzej Rostworowski This is my paper · ORCID
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keywords spectrumasymptoticallyinstabilitylinearnondispersiveperturbationsphyssolution
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We calculate the spectrum of linear perturbations of standing wave solutions discussed in [Phys. Rev. D 87, 123006 (2013)], as the first step to investigate the stability of globally regular, asymptotically AdS, time-periodic solutions discovered in [Phys. Rev. Lett. 111 051102 (2013)]. We show that while this spectrum is only asymptotically nondispersive (as contrasted with the pure AdS case), putting a small standing wave solution on the top of AdS solution indeed prevents the turbulent instability. Thus we support the idea advocated in previous works that nondispersive character of the spectrum of linear perturbations of AdS space is crucial for the conjectured turbulent instability.

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    Neumann boundary conditions in anti-de Sitter space admit non-collapsing, multi-mode scalar solutions with arbitrarily small amplitude despite a fully resonant spectrum.

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