AdS (in)stability: Lessons from the scalar field

Basu, Prabir; Krishnan, Chethan; Subramanian, P. N. Bala

doi:10.1016/j.physletb.2015.05.009

Cited by 29 publications

(39 citation statements)

References 19 publications

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“…Selection rules that restrict energy transfer to higher modes (and 'inverse energy cascades') have been found in [13], [12], [26] and more recently, [14]. Similar quasiperiodic behaviour/selection rules have been seen in a system of gravity and self-interacting scalar fields [41], [42], [43], [44]. At first glance, this is puzzling, since we generically expect a resonant instability in AdS, due to its spectrum.…”

Section: Ii5 Discussion On Further Nonlinear Aspectsmentioning

confidence: 56%

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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Section: Ii5 Discussion On Further Nonlinear Aspectsmentioning

confidence: 56%

Necessary conditions for an AdS-type instability

Menon

Suneeta

2016

Phys. Rev. D

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“…6 and 7 where we compare the energy spectrum and the growth of the Ricci scalar at the origin computed in parallel using the full Einstein equations and the resonant system. On the other hand, the resonant approximation does not work so well for the phases 7 . For this reason (and because of possible breakdown of the cubic approximation near collapse), it is not clear to us what (if any) is the physical interpretation of the oscillatory singularity for the resonant system 8 .…”

Section: Discussionmentioning

confidence: 97%

Resonant Dynamics and the Instability of Anti–de Sitter Spacetime

2015

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We consider spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant in five dimensions and analyze evolution of small perturbations of anti-de Sitter spacetime using the recently proposed resonant approximation. We show that for typical initial data the solution of the resonant system develops an oscillatory singularity in finite time. This result hints at a possible route to establishing instability of AdS under arbitrarily small perturbations.Introduction. A few years ago two of us gave numerical evidence that anti-de Sitter (AdS) spacetime in four dimensions is unstable against black hole formation for a large class of arbitrarily small perturbations [1]. More precisely, we showed that for a perturbation with amplitude ε a black hole forms on the timescale O(ε −2 ). Using nonlinear perturbation analysis we conjectured that the instability is due to the turbulent cascade of energy from low to high frequencies. This conjecture was extended to higher dimensions in [2].Since the computational cost of numerical simulations rapidly increases with decreasing ε, our conjecture was based on extrapolation of the observed scaling behavior of solutions for small (but not excessively so) amplitudes, which left some room for doubts whether the instability will persist to arbitrarily small values of ε (see e.g.[3]). To resolve these doubts, in this paper we validate and reinforce the above extrapolation with the help of a recently proposed resonant approximation [4][5][6]. The key feature of this approximation is that the underlying infinite dynamical system (hereafter referred to as the resonant system) is scale invariant: if its solution with amplitude 1 does something at time t, then the corresponding solution with amplitude ε does the same thing at time t/ε 2 . Moreover, the latter solution remains close to the true solution (starting with the same initial data) for times ε −2 (provided that the errors due to omission of higher order terms do not pile up too rapidly). Thus, by solving the resonant system we can probe the regime of arbitrarily small perturbations (whose outcome of evolution is beyond the possibility of numerical verification).For concreteness, in this paper we focus our attention on AdS 5 (the most interesting case from the viewpoint of AdS/CFT correspondence); an extension to other dimensions is straightforward and will be presented elsewhere.

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“…gravity in AdS [20][21][22][23][24][25][26], which should be understood in the context of thermalization in the gauge theory. It will be interesting to try and fit these two perspectives into a coherent whole.…”

Section: Jhep06(2016)139mentioning

confidence: 99%

Phases of global AdS black holes

Basu

Krishnan

Subramanian

2016

J. High Energ. Phys.

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Abstract:We study the phases of gravity coupled to a charged scalar and gauge field in an asymptotically Anti-de Sitter spacetime (AdS 4 ) in the grand canonical ensemble. For the conformally coupled scalar, an intricate phase diagram is charted out between the four relevant solutions: global AdS, boson star, Reissner-Nordstrom black hole and the hairy black hole. The nature of the phase diagram undergoes qualitative changes as the charge of the scalar is changed, which we discuss. We also discuss the new features that arise in the extremal limit.

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AdS (in)stability: Lessons from the scalar field

Cited by 29 publications

References 19 publications

Necessary conditions for an AdS-type instability

Necessary conditions for an AdS-type instability

Resonant Dynamics and the Instability of Anti–de Sitter Spacetime

Phases of global AdS black holes

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