Three-dimensional Gravity and Instability of AdS$_{3}$

Jałmużna, Joanna

doi:10.5506/aphyspolb.44.2603

Cited by 9 publications

(9 citation statements)

References 22 publications

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“…In addition we have 7 irremovable secular resonances with quantum numbers found in the normal mode spectra ( 5) and ( 7), but that do not coincide with the data (12), { , m, p, ω} s = {6, 6, 1, 9/L}, {8, 6, 0, 9/L} ; { , m, p, ω} s = {8, 8, 2, 13/L}, {10, 8, 1, 13/L}, {12, 8, 0, 13/L} ; { , m, p, ω} v = {9, 8, 1, 13/L}, {11, 8, 0, 13/L} . (13) Here, the first line resonances are of the type 2ω 7 − ω7 = 9/L and coincide with those in the last column of Table II when we start with the single normal mode { , m, p, ω} v = {7, 6, 0, 9/L}. However, the second and third line resonances are of the type 2ω 7 − ω4 = 13/L and thus a consequence of the two-mode collision (12).…”

supporting

confidence: 69%

AdS nonlinear instability: moving beyond spherical symmetry

Dias¹,

Santos²

2016

Class. Quantum Grav.

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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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confidence: 69%

AdS nonlinear instability: moving beyond spherical symmetry

Dias¹,

Santos²

2016

Class. Quantum Grav.

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“…The top panel of figure 8 shows the turbulent energy cascade for the µ = √ 10 and = 0.02. While we cannot rule out that inverse cascades appear at lower amplitudes, we note that this initial data already appears to be in the perturbative regime, as Π 2 (t, x = 0) obeys the perturbative scaling law, 8 as we see in the bottom panel of figure 8. This suggests that AdS 5 may have smaller stable regions around single mode data than AdS 4 , at least for the values of µ we considered.…”

Section: Robustness Against Change Of Profile Shapementioning

confidence: 78%

“…The original studies of massless scalar field matter have since been followed by studies of complex scalar fields [5] and modified theories of gravity [6]. Except when there is a mass gap in the black hole spectrum (such as AdS 3 [7,8] or AdS 5 Einstein-Gauss-Bonnet gravity [6]), these numerical studies have pointed to instability to horizon formation at arbitrarily small amplitudes for generic initial data, which occurs along with a cascade of energy into high frequency modes. On the other hand, certain initial data appear stable at low amplitudes, and additional types of initial data are the subject of some disagreement (see [9][10][11]).…”

Section: Introductionmentioning

confidence: 99%

Classes of stable initial data for massless and massive scalars in Anti-de Sitter spacetime

Deppe

Frey

2015

J. High Energ. Phys.

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Since horizon formation in global anti-de Sitter spacetime is dual to thermalization of a conformal field theory on a compact space, whether generic initial data is stable or unstable against gravitational collapse is of great interest. We argue that all the known stable initial data for massless scalars are dominated by single scalar eigenmodes, specifically providing strong numerical evidence consistent with the interpretation that initial data with equal energies in two modes collapse on time scales of order the inverse square of the amplitude. We further scan the parameter space for massive scalar field initial data and present evidence for a novel class of stable or quasi-stable solutions for massive scalars with energy spread through several eigenmodes.

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“…We see that localization increases with dimension, and is least for d = 2 (AdS 3 ). In AdS 3 , numerical studies show a very fast transfer of energy to higher frequencies (in comparison to higher dimensions), yet no black hole formation [3], [4]. We speculate that at least part of the reason may be that the eigenfunctions localize the least in three dimensions.…”

Section: Asymptotics Of Jacobi Polynomials and Significance For Lmentioning

confidence: 82%

Necessary conditions for an AdS-type instability

Menon

Suneeta

2016

Phys. Rev. D

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In this work, we analyze the necessary conditions for a nonlinear AdS-type instability in the gravity-scalar field system. In particular, we discuss the necessary conditions for a cascade of energy to higher modes by applying results in KAM theory. Our analytical framework explains numerical observations of instability of spacetimes even when the spectrum is only asymptotically resonant, and the fact that a minimum field amplitude is needed to trigger it. Our framework can be applied for similar stability analyses of fields in (locally) asymptotically AdS spacetimes. We illustrate this with the example of the AdS soliton. Further, we conjecture on the possible reasons for quasiperiodic behaviour observed in perturbations of AdS spacetime. Certain properties of the eigenfunctions of the linear system dictate whether there will be localization in space leading to black hole formation. These properties are examined using the asymptotics of Jacobi polynomials. Finally we discuss recent results on the AdS instability in Einstein-Gauss-Bonnet gravity in light of our work.

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Three-dimensional Gravity and Instability of AdS$_{3}$

Abstract: This is an extended version of my lecture at the LIII Cracow School of Theoretical Physics in Zakopane in which I presented the results of joint work with Piotr Bizoń [1] concerning (in)stability of the threedimensional anti-de Sitter spacetime.

Cited by 9 publications

References 22 publications

AdS nonlinear instability: moving beyond spherical symmetry

AdS nonlinear instability: moving beyond spherical symmetry

Classes of stable initial data for massless and massive scalars in Anti-de Sitter spacetime

Necessary conditions for an AdS-type instability

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