Quasi-Local Energy-Momentum and Angular Momentum in General Relativity

Szabados, László

doi:10.12942/lrr-2009-4

Cited by 313 publications

(396 citation statements)

References 491 publications

(960 reference statements)

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“…If naked singularities can still be realized in the quantum realm, they must be described in a qualitatively different way from the present one. 9 Let us now plug the effective mass (3.27) into Eq. (3.19),…”

Section: Single Eigenstatesmentioning

confidence: 99%

Horizon quantum mechanics of rotating black holes

et al. 2017

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The horizon quantum mechanics is an approach that was previously introduced in order to analyze the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. In this work, we first extend the formalism to general spacetimes with asymptotic (ADM) mass and angular momentum. We then apply the extended horizon quantum mechanics to a harmonic model of rotating corpuscular black holes. We find that simple configurations of this model naturally suppress the appearance of the inner horizon and seem to disfavor extremal (macroscopic) geometries.

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Section: Single Eigenstatesmentioning

confidence: 99%

Horizon quantum mechanics of rotating black holes

et al. 2017

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“…II). The vector P is known as the Noether current associated with the symmetry generator η [31,32]. It is conserved in the sense that…”

Section: A Energy Conservationmentioning

confidence: 99%

Extracting black-hole rotational energy: The generalized Penrose process

et al. 2014

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In the case involving particles the necessary and sufficient condition for the Penrose process to extract energy from a rotating black hole is absorption of particles with negative energies and angular momenta. No torque at the black-hole horizon occurs. In this article we consider the case of arbitrary fields or matter described by an unspecified, general energy-momentum tensor Tµν and show that the necessary and sufficient condition for extraction of a black hole's rotational energy is analogous to that in the mechanical Penrose process: absorption of negative energy and negative angular momentum. We also show that a necessary condition for the Penrose process to occur is for the Noether current (the conserved energy-momentum density vector) to be spacelike or past directed (timelike or null) on some part of the horizon. In the particle case, our general criterion for the occurrence of a Penrose process reproduces the standard result. In the case of relativistic jetproducing "magnetically arrested disks" we show that the negative energy and angular-momentum absorption condition is obeyed when the Blandford-Znajek mechanism is at work, and hence the high energy extraction efficiency up to ∼ 300% found in recent numerical simulations of such accretion flows results from tapping the black hole's rotational energy through the Penrose process. We show how black-hole rotational energy extraction works in this case by describing the Penrose process in terms of the Noether current.

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“…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.…”

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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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Quasi-Local Energy-Momentum and Angular Momentum in General Relativity

Cited by 313 publications

References 491 publications

Horizon quantum mechanics of rotating black holes

Horizon quantum mechanics of rotating black holes

Extracting black-hole rotational energy: The generalized Penrose process

Penrose inequality in anti–de Sitter space

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