Positive mass theorems for asymptotically de Sitter spacetimes

Luo, M. X.; Xie, Naqing; Zhang, Xiao

doi:10.1016/j.nuclphysb.2009.09.017

Cited by 19 publications

(32 citation statements)

References 31 publications

(76 reference statements)

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“…Although in certain special cases the positivity of the AD energy can be proven [55,57,48], in general it can have any sign [56,58]. Indeed, in the light of the results of [50] on the energy flux through I + of the linear gravitational perturbations preserving the intrinsic conformal flatness of I + (see subsection 2.2.1), this notion of energy does not seem to have the rigidity property.…”

Section: The Abbott-deser Energy-momentummentioning

confidence: 99%

“…Nevertheless, this can still be called 'energy', but its interpretation is not so obvious. For alternative forms of this energy expression see [21] and (under additional conditions) [57,48].…”

Section: The Abbott-deser Energy-momentummentioning

confidence: 99%

“…The hypersurfaces Σ T := {T = const}, given in the coordinates (T, R, θ, φ) defined by cosh(T /α) := cosh(t/α) cos r, sinh(T /α) cosh R := sinh(t/α) (see e.g [48]…”

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confidence: 99%

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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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Section: The Abbott-deser Energy-momentummentioning

confidence: 99%

Section: The Abbott-deser Energy-momentummentioning

confidence: 99%

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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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“…Even through, the formulations of the positivity are incomplete, and some of the proofs do not seem correct in mathematics. In [38,37], the complete and rigorous study of the positive energy theorem were provided.…”

Section: λ >0mentioning

confidence: 99%

Recent progress on the positive energy theorem

Zhang

2015

Int. J. Mod. Phys. A

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“…erroneous claims of violations of weak cosmic censorship in the literature, as pointed out in [30]; such claims have been disproved by [13]. In the asymptotically de Sitter (dS) case, on the other hand, there exists neither a generally accepted notion of total mass (see however [31,32]) nor a Killing vector field which is timelike in the asymptotic region, and so it is not clear how one should compute the energy of the test matter falling into the black hole. The main purpose of the present paper is to address this issue, and, as a result, to extend the results in [25] to asymptotically dS black holes.…”

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Test fields cannot destroy extremal de Sitter black holes

Natário

Vicente

2020

Gen Relativ Gravit

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We determine the timelike Killing vector field that gives the correct definition of energy for test fields propagating in a Kerr-Newman-de Sitter spacetime, and use this result to prove that test fields cannot destroy extremal Kerr-Newman-de Sitter black holes. IntroductionIn a famous paper [1], Wald tested the weak cosmic censorship conjecture [2, 3] by dropping charged and/or spinning test particles into the event horizon of an extremal Kerr-Newman black hole. Both him and subsequent authors [4,5] found that the particle would not go in for values of the conserved quantities (energy, angular momentum, charge and/or spin) which would overspin/overcharge the black hole. Similar conclusions were reached by analyzing scalar and electromagnetic test fields propagating in extremal Kerr-Newman black hole backgrounds [6,7,8,9]. In this case, the fluxes of energy, angular momentum and charge across the event horizon were found to be always insufficient to overspin/overcharge the black hole. Some of these results were extended to higher dimensions [10,11,12] and also to the case when there is a negative cosmological constant [13,14,15]. At the same time, it was noticed that Wald's thought experiment might produce naked singularities when applied to nearly extremal black holes [16,17,18,19]. However, in this case the perturbation could not be assumed to be infinitesimal, and so backreaction effects would have to be taken into account; when this was done, the validity of the cosmic censorship conjecture appeared to be restored [20,21,22,23,24].In [25], the authors (in collaboration with L. Queimada) gave a general argument showing that extremal Kerr-Newman and Kerr-Newman-anti-de Sitter black holes cannot be overspun/overcharged by any type of test matter satisfying the null energy condition at the event horizon. This argument was later extended by Sorce and Wald [26] to the case of quasi-extremal Kerr-Newman black holes by considering the second order variation of the black hole mass.In all these gedanken experiments, however, one must be very careful with what is meant by the energy of the test matter, and how it relates to the increase in the black hole mass. In fact, from a logical point of view, these are independent concepts: the energy of the test matter is computed with respect to a given timelike Killing vector field, whereas the black hole mass is a parameter in a black hole solution of the Einstein-Maxwell field equations. In the asymptotic flat case, the two can be related via the ADM mass: indeed, the ADM mass of a spacetime containing an isolated black hole is precisely the black hole mass, whereas the energy of test matter located in the asymptotically flat region (measured with respect to the unique timelike Killing vector field) simply adds to the ADM mass; since this energy is conserved as the test matter moves into the black hole spacetime, the black hole mass should increase by precisely that amount when the test matter is absorbed. In the non-asymptotically flat cases, however, there is no ADM mass, an...

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Positive mass theorems for asymptotically de Sitter spacetimes

Cited by 19 publications

References 31 publications

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

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

Recent progress on the positive energy theorem

Test fields cannot destroy extremal de Sitter black holes

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