Gravitational turbulent instability of anti-de Sitter space

Dias, Óscar J. C.; Horowitz, Gary T.; Santos, Jorge E.

doi:10.1088/0264-9381/29/19/194002

Cited by 175 publications

(394 citation statements)

References 16 publications

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“…Since these BHs are time-periodic and single out a particular frequency, we call them black resonators. One limit of black resonators corresponds to the onset of the superradiant instability.Black resonators are thus the BHs predicted by [26] and alluded to in [20,24,27]. The opposite, zero-size limit of black resonators corresponds to the geons where this frequency is given by a nonlinear normal mode of AdS [24,25].…”

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confidence: 85%

“…There is numerical evidence in support of this instability with a spherically symmetric scalar field [21][22][23]. There is additionally a proposed perturbative explanation for this instability [21] which applies to pure gravity and beyond spherical symmetry [24]. At linear order in perturbation theory, AdS contains an infinite tower of evenly-spaced normal modes.…”

Section: Jhep12(2015)171mentioning

confidence: 99%

“…This leads to a family of horizonless time-periodic solutions called oscillons (boson stars) for a real (complex) scalar field [21,22] and geons for pure gravity [24,25]. These geons can be thought of as nonlinear normal modes of AdS and are solutions that contain only a single Killing field.…”

Section: Jhep12(2015)171mentioning

confidence: 99%

“…Any gravitational radiation emitted by the geon is balanced by absorption of waves reflected from the AdS boundary. Since perturbation theory breaks down for twomode initial data, geons can be thought of as a basis for the nonlinear instability [24,25].We will construct a new family of BHs that joins the onset of the superradiant instability of 20] 1 to the geons. Since these BHs are time-periodic and single out a particular frequency, we call them black resonators.…”

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Black holes with a single Killing vector field: black resonators

Dias

Santos

Way

2015

J. High Energ. Phys.

144

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Abstract:We numerically construct asymptotically anti-de Sitter (AdS) black holes in four dimensions that contain only a single Killing vector field. These solutions, which we coin black resonators, link the superradiant instability of Kerr-AdS to the nonlinear weakly turbulent instability of AdS by connecting the onset of the superradiance instability to smooth, horizonless geometries called geons. Furthermore, they demonstrate nonuniqueness of Kerr-AdS by sharing asymptotic charges. Where black resonators coexist with Kerr-AdS, we find that the black resonators have higher entropy. Nevertheless, we show that black resonators are unstable and comment on the implications for the endpoint of the superradiant instability.Keywords: Black Holes, AdS-CFT Correspondence, Classical Theories of Gravity JHEP12 (2015)171 Introduction. As the simplest of gravitating objects, black holes (BHs) play a fundamental role in our understanding of general relativity. Indeed, four-dimensional, asymptotically flat BHs are stable and uniquely specified by their asymptotic charges [1]. However, there are circumstances where stability and uniqueness can be violated, such as those in higher dimensions [2][3][4][5][6][7][8][9][10][11]. We will argue that this can also be accomplished in four dimensions with asymptotically anti-de Sitter (AdS) BHs. Unlike Minkowski or de Sitter space, AdS contains a timelike boundary at conformal infinity where reflecting (energy and angular momentum conserving) boundary conditions are typically imposed to render the initial value problem well posed [12]. The presence of this boundary has drastic consequences for the stability of solutions in AdS. For example, rotating BHs may contain an ergoregion from which energy can be extracted by the Penrose process [13]. For waves, this phenomenon is called superradiance [14][15][16] (see [17] for a review). In AdS, these waves return after scattering from the boundary and extract more energy. The process continues until the waves contain enough energy to backreact on the geometry, causing the so-called superradiant instability [18][19][20].The reflecting boundary also has implications for the stability of AdS itself. A nonlinear instability may occur if an excitation with arbitrarily small, but finite energy around AdS continues to reflect off the boundary and eventually forms a BH. There is numerical evidence in support of this instability with a spherically symmetric scalar field [21][22][23]. There is additionally a proposed perturbative explanation for this instability [21] which applies to pure gravity and beyond spherical symmetry [24]. At linear order in perturbation theory, AdS contains an infinite tower of evenly-spaced normal modes. At higher orders, resonances between modes cause higher modes to be excited that grow linearly in time. In the generic case, this leads to a breakdown of perturbation theory, and is interpreted as the beginnings of a nonlinear instability. This instability is called weakly turbulent due to this energy shift from longer to sho...

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mentioning

confidence: 85%

Section: Jhep12(2015)171mentioning

confidence: 99%

Section: Jhep12(2015)171mentioning

confidence: 99%

mentioning

confidence: 99%

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Black holes with a single Killing vector field: black resonators

Dias

Santos

Way

2015

J. High Energ. Phys.

144

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“…Weak turbulence versus inverse cascade. In parallel with the perturbative analysis [5,10,13], recent simulations have identified an inverse-cascade effect as the responsible for halting the collapse and leading to dynamical, nondispersive solutions [7] (but see [8]). Large families of initial data exist whose late-time evolution is characterized by energy transfer to lower frequencies, thus being competitive to weak turbulence 3 .…”

Section: A Open Questions and Executive Summarymentioning

confidence: 99%

Study of the nonlinear instability of confined geometries

2014

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The discovery of a "weakly-turbulent" instability of anti-de Sitter spacetime supports the idea that confined fluctuations eventually collapse to black holes and suggests that similar phenomena might be possible in asymptotically-flat spacetime, for example in the context of spherically symmetric oscillations of stars or nonradial pulsations of ultracompact objects. Here we present a detailed study of the evolution of the Einstein-Klein-Gordon system in a cavity, with different types of deformations of the spectrum, including a mass term for the scalar and Neumann conditions at the boundary. We provide numerical evidence that gravitational collapse always occurs, at least for amplitudes that are three orders of magnitude smaller than Choptuik's critical value and corresponding to more than 10 5 reflections before collapse. The collapse time scales as the inverse square of the initial amplitude in the small-amplitude limit. In addition, we find that fields with nonresonant spectrum collapse earlier than in the fully-resonant case, a result that is at odds with the current understanding of the process. Energy is transferred through a direct cascade to high frequencies when the spectrum is resonant, but we observe both direct-and inverse-cascade effects for nonresonant spectra. Our results indicate that a fully-resonant spectrum might not be a crucial ingredient of the conjectured turbulent instability and that other mechanisms might be relevant. We discuss how a definitive answer to this problem is essentially impossible within the present framework.

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