Instability of Anti-de Sitter Spacetime

Bizoń, Piotr; Rostworowski, Andrzej

doi:10.1007/978-3-319-06349-2_11

Cited by 7 publications

(12 citation statements)

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“…A similar inverse cascade effect has been recently shown to halt collapse for a large family of initial data in AdS because it is competitive to weak turbulence [7] (but see also [8]). However, our initial data are generic and do not necessarily belong to the class discussed in Ref.…”

Section: Direct-and Inverse-cascade Effectsmentioning

confidence: 55%

“…2 in Ref. [8] for a similar convergence test). This definition allows the highly-oscillatory behavior of Π at the center (as shown in the first three plots of Fig.…”

Section: Appendix A: Cartoon Methodsmentioning

confidence: 86%

“…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%

“…7). The latter effect can quench turbulent instability for some configurations [7] (but see [8]). However, our results leave open the possibility that even inverse cascade is not enough to prevent collapse at very late times for generic families of initial data.…”

Section: Do We Understand the Nonlinear Instability Of Confined Gmentioning

confidence: 99%

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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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Section: Direct-and Inverse-cascade Effectsmentioning

confidence: 55%

“…2 in Ref. [8] for a similar convergence test). This definition allows the highly-oscillatory behavior of Π at the center (as shown in the first three plots of Fig.…”

Section: Appendix A: Cartoon Methodsmentioning

confidence: 86%

Section: A Open Questions and Executive Summarymentioning

confidence: 99%

Section: Do We Understand the Nonlinear Instability Of Confined Gmentioning

confidence: 99%

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Study of the nonlinear instability of confined geometries

2014

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“…A useful formula for proving the inequality (10) is the radial mass flow equation obtained by differentiating (18), and using (15) and (16). This gives…”

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confidence: 99%

Penrose inequality in anti–de Sitter space

Husain

Singh

2017

Phys. Rev. D

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For asymptotically flat spacetimes the Penrose inequality gives an initial data test for the weak cosmic censorship hypothesis. We give a formulation of this inequality for asymptotically anti-deSitter (AAdS) spacetimes, and show that the inequality holds for time asymmetric data in spherical symmetry. Our analysis is motivated by the constant-negative-spatial-curvature form of the AdS black hole metric.Keywords: Cosmic Censorship, Penrose Inequality, anti-deSitter spacetime One of the most important unresolved questions in classical general relativity is Penrose's cosmic censorship hypothesis. The weak version of this hypothesis, Weak Cosmic Censorship (WCC), is the statement that a spacetime singularity arising from gravitational collapse of "reasonable" matter must be shrouded by an event horizon [1].Penrose also proposed an "initial data test" suggested by the WCC hypothesis. Consider an asymptotically flat solution of Einstein equations with matter satisfying the dominant energy condition. Then if a Cauchy slice of this solution contains an outer-trapped 2-surface S of area A(S), and if M is the Arnowitt-Deser-Misner (ADM) mass of the data on the slice, the conjectured inequality is(1)The intuition behind this inequality is that the mass m ah contained within the outermost apparent horizon cannot exceed the total mass M of the data. This is expected to be the case for an ongoing gravitational collapse since, in general, the region between this horizon and spatial infinity will contain uncollapsed (positive energy) matter. Thus the inequality may equivalently be written aswith equality in the quiescent black hole state, when all matter has fallen into the horizon. A review of the status of WCC and the Penrose inequality appears in Refs. [2,3] In this paper we study a generalization of this inequality for asymptotically anti-deSitter (AAdS) spacetimes in 4-spacetime dimensions. This requires definitions of AAdS data and quasi-local mass. The former is well known (see eg.[4]), and the latter requires a suitable generalization of one several mass definitions [5] to AAdS. The basic requirement is that any quasi-local mass should give the total mass of data in the asymptotic limit. This is guided by, and tested for, using the Schwarzschild-AdS spacetime.We will use the Hawking mass [6], which has been used to study the Penrose inequality in the asymptotically flat case [7]. This quantity is a measure of the mass contained within a closed 2-surface S in a spatial slice of spacetime. The definition iswhere A S is the area of S and θ ± are the future directed ingoing (−) and outgoing (+) null expansions of S. In terms of the ADM data (q ab , K ab ) these arewhere s a is the unit normal to S. As a prelude to introducing the class of data we will work with, let us note that the AdS black hole may be written in a form analogous to the Painleve-Gulstrand (PG) form, but rather than using the flat-slice PG form for AdS, it is more convenient to work with 3−slices of constant negative curvature. With such a choice of coord...

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