Penrose inequality for asymptotically AdS spaces

Itkin, Igor; Oz, Yaron

doi:10.1016/j.physletb.2012.01.007

Cited by 12 publications

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“…A similar inequality has been conjectured for asymptotically anti-de Sitter (AdS) initial data with an apparent horizon σ [5]. The same arguments involving cosmic censorship and black holes settling down to a stationary solution lead to the conclusion that the mass M and area A[σ] of an asymptotically AdS initial data with apparent horizon σ in 4D should satisfy 2…”

Section: Introductionsupporting

confidence: 58%

“…So far we have been assuming four-dimensional spacetimes, but there is no obstruction to considering the Penrose inequality in higher dimensions. The general form of the Penrose inequality in AdS in higher dimensions is given in [5]; a proof of the Riemannian Penrose inequality for asymptotically flat Riemannian manifolds of dimension less than eight is given in [10]. In higher dimensions, however, the Penrose inequality loses its connection with cosmic censorship, since there are unstable black holes in higher dimensions that develop singularities on their horizon when they pinch off, violating cosmic censorship.…”

Section: Introductionmentioning

confidence: 99%

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Holographic argument for the Penrose inequality in AdS spacetimes

Engelhardt

Horowitz

2019

Phys. Rev. D

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We give a holographic argument in favor of the AdS Penrose inequality, which conjectures a lower bound on the total mass in terms of the area of apparent horizons. This inequality is often viewed as a test of cosmic censorship. We further find a connection between the area law for apparent horizons and the Penrose inequality. Finally, we show that the argument also applies to solutions with charge, resulting in a charged Penrose inequality in AdS.

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Section: Introductionsupporting

confidence: 58%

Section: Introductionmentioning

confidence: 99%

Holographic argument for the Penrose inequality in AdS spacetimes

Engelhardt

Horowitz

2019

Phys. Rev. D

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“…Among the more important is a generalization of our data to axial symmetry in light of recent results hinting at a violation of WCC in AAdS spacetime [17]. This work suggests that it may be possible to construct explicit examples that show violation of (10). Furthermore, in light of the AdS/CFT duality conjecture, an interesting direction would be an exploration of the analog of the inequality in the CFT.…”

mentioning

confidence: 70%

“…There are proposals for the Penrose inequality similar to (10) for AdS spacetimes which use a background subtraction to define a regulated mass. One of these is an extension to include charge [10], but contains no further analysis.…”

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confidence: 99%

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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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Holography abhors visible trapped surfaces

Engelhardt

Folkestad

2021

J. High Energ. Phys.

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We prove that consistency of the holographic dictionary implies a hallmark prediction of the weak cosmic censorship conjecture: that in classical gravity, trapped surfaces lie behind event horizons. In particular, the existence of a trapped surface implies the existence of an event horizon, and that furthermore this event horizon must be outside of the trapped surface. More precisely, we show that the formation of event horizons outside of a strong gravity region is a direct consequence of causal wedge inclusion, which is required by entanglement wedge reconstruction. We make few assumptions beyond the absence of evaporating singularities in strictly classical gravity. We comment on the implication that spacetimes with naked trapped surfaces do not admit a holographic dual, note a possible application to holographic complexity, and speculate on the dual CFT interpretation of a trapped surface.

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Penrose inequality for asymptotically AdS spaces

Cited by 12 publications

References 14 publications

Holographic argument for the Penrose inequality in AdS spacetimes

Holographic argument for the Penrose inequality in AdS spacetimes

Penrose inequality in anti–de Sitter space

Holography abhors visible trapped surfaces

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