Hamiltonian mass of asymptotically Schwarzschild–de Sitter space-times

Chruściel, Piotr T.; Jezierski, Jacek; Kijowski, Jerzy

doi:10.1103/physrevd.87.124015

Cited by 18 publications

(27 citation statements)

References 16 publications

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“…As already discussed in [13], in the case of a positive cosmological constant there does not seem to be a general consensus about what the right notion of mass should be. For some possible approaches, as well as for more insights on the problems posed by the case Λ > 0, we refer the reader to the following references [1,6,7,8,22,34,43,50,51,54]. In our previous work [13], we have introduced a different point of view, leading to a new notion of mass, that we now recall.…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

On the Mass of Static Metrics with Positive Cosmological Constant: II

Borghini

Mazzieri

2020

Commun. Math. Phys.

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This is the second of two works, in which we discuss the definition of an appropriate notion of mass for static metrics, in the case where the cosmological constant is positive and the model solutions are compact. In the first part, we have established a positive mass statement, characterising the de Sitter solution as the only static vacuum metric with zero mass. In this second part, we prove optimal area bounds for horizons of black hole type and of cosmological type, corresponding to Riemannian Penrose inequalities and to cosmological area bounds à la Boucher–Gibbons–Horowitz, respectively. Building on the related rigidity statements, we also deduce a uniqueness result for the Schwarzschild–de Sitter spacetime.

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Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

On the Mass of Static Metrics with Positive Cosmological Constant: II

Borghini

Mazzieri

2020

Commun. Math. Phys.

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“…In this subsection we review their work on asymptotically-Schwarzschild-de Sitter data and asymptotically-Kerr-de Sitter data. These are discussed in [60] and [61] respectively and these in turn rely on families of initial data for the Einstein equations shown to exist in [62] and [63] respectively. The Schwarzschild-de Sitter metric, sometimes called the Kottler solution, can be defined in space-time dimension n + 1 as…”

Section: Asymptotically-schwarzschild/kerr-de Sitter Data: Work Of Chmentioning

confidence: 99%

“…These ends can then in turn be truncated and glued on to other regions to produce data on connected sums or wormholes. In [60], the authors use the Hamiltonian method to assign masses to the simplest case of initial data in this class, a single region with several Delaunay ends. The result is that the Hamiltonian mass of each end is precisely the mass parameter m in the appropriate metric (3.5) (and a fortiori it is positive).…”

Section: )mentioning

confidence: 99%

A review of total energy–momenta in GR with a positive cosmological constant

Szabados

Paul

2019

Int. J. Mod. Phys. D

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A review is given of the various approaches to and expressions for total energymomentum and mass in the presence of a positive cosmological constant in Einstein's field equations, together with a discussion of the key conceptual questions, main ideas and techniques behind them. * Dedicated to our friend, Jörg Frauendiener, on the occasion of his 60th birthday.Ach, wie schön muss sich's ergehen, Dort in Newmans Himmelsraum. Und Lichtkugeln auf den Höhen -O wie lab'n sie meinen Traum ! from Ein theoretisch-physikalischer Schiller-Traum by N. V. Mitskievitch future of the point with Cartesian coordinates (τ, 0, 0, 0). All the leaves of this latter foliation intersect the future null infinity at one and the same cut u = τ , rather than providing a foliation of the null infinity (see Fig. 1.iii.).3 This can be proved, given certain causality assumptions; see [16].

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“…The coefficient 1 6π 2 arises from the volume of three-dimensional sphere and from the coefficient in the Einstein equation in this dimension (see Appendix D in [5]). More precisely, 2γ = 2(n − 1)ω n−1 n − 2 = 16π for n = 3 6π 2 for n = 4 .…”

Section: 1 Energy As the Mass Chargementioning

confidence: 99%

Conformal Yano--Killing Tensors for Space-times with Cosmological Constant

Czajka¹,

Jezierski²

2018

Acta Phys. Pol. B

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We present a new method for constructing conformal Yano-Killing tensors in five-dimensional Anti-de Sitter space-time. The found tensors are represented in two different coordinate systems. We also discuss, in terms of CYK tensors, global charges which are well defined for asymptotically (five-dimensional) Anti-de Sitter space-time. Additionally in Appendix we present our own derivation of conformal Killing one-forms in four-dimensional Anti-de Sitter space-time as an application of the Theorem 4.

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Hamiltonian mass of asymptotically Schwarzschild–de Sitter space-times

Cited by 18 publications

References 16 publications

On the Mass of Static Metrics with Positive Cosmological Constant: II

On the Mass of Static Metrics with Positive Cosmological Constant: II

A review of total energy–momenta in GR with a positive cosmological constant

Conformal Yano--Killing Tensors for Space-times with Cosmological Constant

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