Superradiant instabilities of asymptotically anti-de Sitter black holes

Green, Stephen; Hollands, Stefan; Ishibashi, Akihiro; Wald, Robert M.

doi:10.1088/0264-9381/33/12/125022

Cited by 67 publications

(80 citation statements)

References 46 publications

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“…The reason for this is that small black resonators are well-approximated (as confirmed in (9) and figure 2) by a small Kerr-AdS BH at the centre of a geon [20,24], and small Kerr-AdS BHs are still unstable to higher m modes. More precisely, the results of [38] mathematically prove that our solutions are unstable, since no Killing vector field that is everywhere timelike can be found at the conformal boundary.…”

Section: ��mentioning

confidence: 80%

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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Section: ��mentioning

confidence: 80%

Black holes with a single Killing vector field: black resonators

Dias

Santos

Way

2015

J. High Energ. Phys.

144

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“…This region is therefore a natural place to study the rotational superradiant instability [65,[76][77][78][79][80][81][82] for which little is known fully dynamically. However, typical growth rates for this instability are around 10 −5 [68], which requires a longer simulation than we can feasibly perform with our methods.…”

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confidence: 99%

“…Furthermore, our ansatz implies that such a study will necessarily be incomplete. High angular wavenumbers are expected to play an important role in this instability [65,[80][81][82], but our ansatz is restricted to only the m = 1 azimuthal wavenumbers. …”

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confidence: 99%

Collapse and Nonlinear Instability of AdS Space with Angular Momentum

et al. 2017

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We present a numerical study of rotational dynamics in AdS5 with equal angular momenta in the presence of a complex doublet scalar field. We determine that the endpoint of gravitational collapse is a Myers-Perry black hole for high energies and a hairy black hole for low energies. We investigate the timescale for collapse at low energies E, keeping the angular momenta J ∝ E in AdS length units. We find that the inclusion of angular momenta delays the collapse time, but retains a t ∼ 1/E scaling. We perturb and evolve rotating boson stars, and find that boson stars near AdS appear stable, but those sufficiently far from AdS are unstable. We find that the dynamics of the boson star instability depend on the perturbation, resulting either in collapse to a Myers-Perry black hole, or development towards a stable oscillating solution.Introduction -Spacetimes with anti-de Sitter (AdS) boundary conditions play a central role in our understanding of gauge/gravity duality [1][2][3][4], where solutions to the Einstein equation with a negative cosmological constant are dual to states of strongly coupled field theories. This correspondence has inspired the study of gravitational physics in AdS over the past two decades.It is perhaps surprising that the issue of the nonlinear stability of (global) AdS was only raised nine years after AdS/CFT was first formulated [5,6]. Dafermos and Holzegel conjectured a nonlinear instability where the reflecting boundary of AdS allows for small but finite energy perturbations to grow and eventually collapse into a black hole. This is in stark contrast with Minkowksi and de Sitter spacetimes, where nonlinear stability has long been established [7,8].The first numerical evidence in favour of such an instability of AdS was reported in [9]. This topic has since attracted much attention both from numerical and formal perspectives . Remarkably, this instability has recently been proved for the spherically symmetric and pressureless Einstein-massless Vlasov system [62,63].The collapse timescale is dual to the thermalisation time in the field theory, and is important for characterising and understanding this instability. For energies E much smaller than the AdS length L = 1, early evolution is well-described by perturbation theory. However, irremovable resonances generically cause secular terms to grow, leading to a breakdown of perturbation theory at a time t ∼ 1/E. Numerical evidence suggests that horizon formation occurs shortly thereafter, i.e. at this same timescale. It is not fully understood why collapse seems to occur at the shortest timescale allowed by perturbation theory, though see [52] for some recent progress.However, all numerical studies have been restricted to zero angular momentum. Though perturbation theory breaks down at t ∼ 1/E for systems with rotation as well [10,53,64], this only places a lower bound on the timescale for gravitational collapse. It therefore remains unclear whether rotational forces could balance the gravitational attraction and delay the collapse time.The inc...

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“…When the rotation boundary parameter ε is larger than a critical value ε = 2, the Killing vector ∂ t becomes spacelike for certain regions of θ with ε > 2, which are so called as ergoregions. For ε > 2, both solitons and black holes develop hair due to superradiance, and the spacetime with ergoregions in AdS may be unstable due to the superradiant scattering [16]. Furthermore, a family of deforming vacuum solutions with a noncompact, differential rotation boundary metric was numerically studied in [17].…”

Section: Introductionmentioning

confidence: 99%

Deforming black holes with odd multipolar differential rotation boundary

Sun

et al. 2019

Phys. Rev. D

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Motivated by the novel asymptotically global AdS 4 solutions with deforming horizon in [JHEP 1802[JHEP , 060 (2018], we analyze the boundary metric with odd multipolar differential rotation and numerically construct a family of deforming solutions with tripolar differential rotation boundary, including two classes of solutions: solitons and black holes. We find that the maximal values of the rotation parameter ε, below which the stable large black hole solutions could exist, are not a constant for T > T schw = √ 3/2π 0.2757. When temperature is much higher than T schw , even though the norm of Killing vector ∂ t keeps timelike for some regions of ε < 2, solitons and black holes with tripolar differential rotation could be unstable and develop hair due to superradiance. As the temperature T drops toward T schw , we find that though there exists the spacelike Killing vector ∂ t for some regions of ε > 2, solitons and black holes still exist and do not develop hair due to superradiance. Moreover, for T T schw , the curves of entropy firstly combine into one curve and then separate into two curves again, in the case of each curve there are two solutions at a fixed value of ε. In addition, we study the deformations of horizon for black holes by using an isometric embedding in the hyperbolic three-dimensional space. Furthermore, we also study the quasinormal modes of the solitons and black holes, which have analogous behaviours to that of dipolar rotation and quadrupolar rotation. *

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Superradiant instabilities of asymptotically anti-de Sitter black holes

Cited by 67 publications

References 46 publications

Black holes with a single Killing vector field: black resonators

Black holes with a single Killing vector field: black resonators

Collapse and Nonlinear Instability of AdS Space with Angular Momentum

Deforming black holes with odd multipolar differential rotation boundary

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