A toy Penrose inequality and its proof

Bengtsson, Ingemar; Jakobsson, Emma

doi:10.1007/s10714-016-2155-x

Cited by 7 publications

(5 citation statements)

References 23 publications

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“…Ref. [12] contains a formulation and proof in 2+1 AdS spacetime; Ref. [13] studies the generalized Hawking mass in a holographic context using the technique of inverse mean curvature (IMC) flow (see also [14] where IMC flow with Hawking mass is suggested as a means for proving Penrose inequalities).…”

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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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confidence: 99%

Penrose inequality in anti–de Sitter space

Husain

Singh

2017

Phys. Rev. D

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“…Due to its simplicity, many toy models in (2 + 1)-dimensions are used to help us gain insights into the corresponding physics in higher dimensions. A recent example is a toy model of the Riemannian Penrose inequality, which has been proved in (2 + 1)-dimensions in AdS background [43] (there is still no general proof for the inequality in (3 + 1)-dimensions). BTZ black holes have also found some surprising applications, e.g., in modeling the physics of graphene [44,45], via the optical metric approach.…”

Section: Photon Orbits On the Horizons Of Extremal Ads 3 Black Holesmentioning

confidence: 99%

Lux in obscuro II: photon orbits of extremal AdS black holes revisited

Tang

Ong

Wang

2017

Class. Quantum Grav.

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A large class of spherically symmetric static extremal black hole spacetimes possesses a stable null photon sphere on their horizons. For the extremal Kerr-Newman family, the photon sphere only really coincides with the horizon in the sense clarified by Doran. The condition under which photon orbit is stable on an asymptotically flat extremal Kerr-Newman black hole horizon has recently been clarified; it is found that a sufficiently large angular momentum destabilizes the photon orbit, whereas electrical charge tends to stabilize it. We investigated the effect of a negative cosmological constant on this observation, and found the same behavior in the case of an extremal asymptotically Kerr-Newman-AdS black holes in (3 + 1)-dimensions. In (2 + 1)-dimensions, in the presence of electrical charge, the angular momentum never becomes large enough to destabilize the photon orbit. We comment on the instabilities of black hole spacetimes with a stable photon orbit.

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“…The first black hole solution is BTZ(Bañados, Teitelboim and Zanelli) solution [35,36], which is asymptotically anti-de Sitter(AdS) and has on curvature singularity. However, it is a genuine black hole solution due to the presence of event horizon, Hawking radiation, entropy, and playing a significant role to understand physical properties in higher dimensions by using many of toy models [37,38]. The black hole thermodynamics has raised some challenging questions: a statistical derivation of black hole entropy and an account of its microstates.…”

Section: Introductionmentioning

confidence: 99%

Rotating BTZ-like black hole and central charges in Einstein-bumblebee gravity

Ding¹,

Yu²,

Zhou³

et al. 2023

Preprint

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We obtain an exact rotating BTZ-like black hole solution by solving the corresponding gravitational field equations in Einstein-bumblebee gravity theory. Result is presented for the purely radial Lorentz symmetry violating. This black hole has two horizons and an ergosphere which are independent on the bumblebee coupling constant ℓ. We study the AdS/CFT correspondence of this black hole, find that the entropy product of its inner and outer horizons is universal. So the central charges of the dual CFT on the boundary can be obtained via the thermodynamic method, and they can reappear black hole mass and angular momentum in the bulk.

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A toy Penrose inequality and its proof

Cited by 7 publications

References 23 publications

Penrose inequality in anti–de Sitter space

Penrose inequality in anti–de Sitter space

Lux in obscuro II: photon orbits of extremal AdS black holes revisited

Rotating BTZ-like black hole and central charges in Einstein-bumblebee gravity

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