The University of Southampton
University of Southampton Institutional Repository

AdS nonlinear instability: breaking spherical and axial symmetries

AdS nonlinear instability: breaking spherical and axial symmetries
AdS nonlinear instability: breaking spherical and axial symmetries
Considerable effort has been dedicated to study the nonlinear instability of Anti-de Sitter (AdS) within spherical symmetry, but little is known about this nonlinear instability in the purely gravi- tational sector, where spherical symmetry is necessarily broken. In [1] the onset of such nonlinear instability was associated with the existence of irremovable secular resonances at third order in perturbation theory. Furthermore, it was also conjectured in [1] that certain very fine tuned initial data would not collapse. Such solutions, upon linearisation, correspond to individual normal modes of AdS, which can be consistently backreacted to all orders in perturbation theory. However, the analysis of [1] was restricted to spherical symmetry. The perturbative arguments of [1] were then generalised to gravitational perturbations in [2], and in particular certain time-periodic solutions were also conjectured to exist - these were coined geons. 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. We also show that weak turbulent perturbative theory predicts the existence of direct and inverse cascades, and give evidence suggesting that the former dominates the latter for equal energy two-mode seeds.
0264-9381
185006
Dias, Óscar J C
f01a8d9b-9597-4c32-9226-53a6e5500a54
Santos, Jorge E
6e5a1703-a14c-4ef6-bfe4-7e4c5177c274
Dias, Óscar J C
f01a8d9b-9597-4c32-9226-53a6e5500a54
Santos, Jorge E
6e5a1703-a14c-4ef6-bfe4-7e4c5177c274

Dias, Óscar J C and Santos, Jorge E (2018) AdS nonlinear instability: breaking spherical and axial symmetries. Classical and Quantum Gravity, 35 (18), 185006. (doi:10.1088/1361-6382/aad514).

Record type: Article

Abstract

Considerable effort has been dedicated to study the nonlinear instability of Anti-de Sitter (AdS) within spherical symmetry, but little is known about this nonlinear instability in the purely gravi- tational sector, where spherical symmetry is necessarily broken. In [1] the onset of such nonlinear instability was associated with the existence of irremovable secular resonances at third order in perturbation theory. Furthermore, it was also conjectured in [1] that certain very fine tuned initial data would not collapse. Such solutions, upon linearisation, correspond to individual normal modes of AdS, which can be consistently backreacted to all orders in perturbation theory. However, the analysis of [1] was restricted to spherical symmetry. The perturbative arguments of [1] were then generalised to gravitational perturbations in [2], and in particular certain time-periodic solutions were also conjectured to exist - these were coined geons. 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. We also show that weak turbulent perturbative theory predicts the existence of direct and inverse cascades, and give evidence suggesting that the former dominates the latter for equal energy two-mode seeds.

Text
1705.03065 - Accepted Manuscript
Download (1MB)

More information

Accepted/In Press date: 23 July 2018
e-pub ahead of print date: 23 July 2018
Published date: 20 September 2018

Identifiers

Local EPrints ID: 423343
URI: http://eprints.soton.ac.uk/id/eprint/423343
ISSN: 0264-9381
PURE UUID: 1fad9d5b-745d-4e9d-9cba-38c9f0c0f4eb
ORCID for Óscar J C Dias: ORCID iD orcid.org/0000-0003-4855-4750

Catalogue record

Date deposited: 20 Sep 2018 16:30
Last modified: 10 Dec 2019 05:13

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×