Critical scalar field collapse in
                    <b>
                      AdS
                      <sub>3</sub>
                    </b>
                    : an analytical approach

Baier, Rudolf; Stricker, Stefan A.; Taanila, Olli

doi:10.1088/0264-9381/31/2/025007

Cited by 12 publications

(27 citation statements)

References 41 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) Here, the first line resonances are of the type 2ω 7 − ω 7 = 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 −ω 4 = 13/L and thus a consequence of the two-mode collision (12).…”

Section: Normal Modes Without a Nonlinear Extension And Geons -At Firsupporting

confidence: 70%

“…(v)7 ε . (12) The first is a scalar mode that in isolation does not develop irremovable resonances, while the second is a vector mode that does so: see Tables I and II. At second order, there are 16 scalar and 13 vector harmonics excited and the solution can be made asymptotically global AdS and regular without introducing resonances. At third order, a total of 34 scalar and 31 vector harmonics are excited.…”

Section: Normal Modes Without a Nonlinear Extension And Geons -At Firmentioning

confidence: 99%

“…It removes a resonance of the type 2ω 4 −ω 4 = 5/L and 2ω 7 −ω 7 = 9/L, respectively. The second contribution is due to the interaction of the initial modes in (12) and is proportional to their relative initial amplitudes. It removes a resonance of the typē ω 4 +ω 7 −ω 7 = 5/L andω 7 +ω 4 −ω 4 = 9/L, respectively.…”

Section: Normal Modes Without a Nonlinear Extension And Geons -At Firmentioning

confidence: 99%

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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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Section: Normal Modes Without a Nonlinear Extension And Geons -At Firsupporting

confidence: 70%

Section: Normal Modes Without a Nonlinear Extension And Geons -At Firmentioning

confidence: 99%

Section: Normal Modes Without a Nonlinear Extension And Geons -At Firmentioning

confidence: 99%

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AdS nonlinear instability: moving beyond spherical symmetry

Dias¹,

Santos²

2016

Class. Quantum Grav.

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“…Using this guide and a direct inspection of (26), we find that at third order the seed (52) 5,7,9,11,13; 7,9,11,13,15; 9, 11, 13, 15, 17; (58) 11, 13, 15. Out of the 30 scalar harmonics (58) there are four that stand out as special because they have a quantum numbers { s , m s , p s , ω} that are already present in the linear frequency spectrum (19). These are…”

Section: Direct and Inverse Turbulent Gravitational Cascadesmentioning

confidence: 99%

AdS nonlinear instability: breaking spherical and axial symmetries

Dias

Santos

2018

Class. Quantum Grav.

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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 gravitational 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. Contents

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“…Due to the symmetries of the setup, there are only two independent components of the energy momentum tensor, T xx = T yy = T zz and T τ τ , where τ refers to the proper time of the shell. Ideally, the shell would be created by momentarily turning on a source term in the boundary theory [36,37], in which case the relation between the two components of T µν , i.e. the EoS of the shell, would be known by construction.…”

mentioning

confidence: 99%

Dynamics of gravitational collapse and holographic entropy production

et al. 2014

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We consider the time evolution of two entropy-like quantities, the holographic entanglement entropy and causal holographic information, in a model of holographic thermalization dual to the gravitational collapse of a thin planar shell. Unlike earlier calculations valid in different limits, we perform a full treatment of the dynamics of the system, varying both the shell's equation of state and initial position. In all cases considered, we find that between an early period related to the acceleration of the shell and a late epoch of saturation towards the thermal limit, the entanglement entropy exhibits universal linear growth in time in accordance with the prediction of Liu and Suh. As intermediate steps of our analysis, we explicitly construct a coordinate system continuous at the location of an infinitely thin shell and derive matching conditions for geodesics and extremal surfaces traversing this region.Introduction. The equilibration dynamics of strongly coupled systems is an active topic of research, motivated equally by studies of the thermalization process of heavy ion collisions and quantum quenches in condensed matter systems (see e.g. [1] for a review). Approaching the problem in the cleanest setup possible -N = 4 Super YangMills (SYM) theory in the limit of large N c and 't Hooft coupling λ -it may be formulated as follows: Given various physically motivated initial conditions, how does the gravitational system evolve towards its final state involving a black hole in AdS 5 space-time? And what are the implications of this gravitational dynamics on the dual field theory side; in particular, how do different physical quantities behave during the equilibration process?In the context of heavy ion physics, recent years have witnessed remarkable progress in the holographic description of the collision. This includes extensive work on colliding shock waves in strongly coupled N = 4 SYM theory [2-6], equilibration in inhomogeneous and anisotropic systems [7][8][9][10][11], and even studies relaxing the assumptions of infinite 't Hooft coupling [12][13][14][15] and conformal invariance [16]. Typical quantities considered in these setups are expectation values of different components of the energy momentum tensor as well as two-point functions related to transport or photon production [17,18]. So far, more complicated observables have been considered only in the simplest setups, such as the quasistatic or Vaidya limits of a gravitationally collapsing planar shell moving either arbitrarily slowly or at the speed of light,

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Critical scalar field collapse in AdS ₃ : an analytical approach

Cited by 12 publications

References 41 publications

AdS nonlinear instability: moving beyond spherical symmetry

AdS nonlinear instability: moving beyond spherical symmetry

AdS nonlinear instability: breaking spherical and axial symmetries

Dynamics of gravitational collapse and holographic entropy production

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Critical scalar field collapse in AdS 3 : an analytical approach

Cited by 12 publications

References 41 publications

AdS nonlinear instability: moving beyond spherical symmetry

AdS nonlinear instability: moving beyond spherical symmetry

AdS nonlinear instability: breaking spherical and axial symmetries

Dynamics of gravitational collapse and holographic entropy production

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Critical scalar field collapse in AdS ₃ : an analytical approach