Geometric Inequalities for Quasi-Local Masses

Alaee, Aghil; Khuri, Marcus; Yau, Shing–Tung

doi:10.1007/s00220-020-03733-0

Cited by 10 publications

(9 citation statements)

References 68 publications

(129 reference statements)

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“…However, since Chen, Wang, and Yau [21] have defined a generalized notion of angular momentum associated with a 2− surface enclosing a space-like domain in s physical spacetime, we intend to extend this study in the future by adopting their technique to explicitly compute the angular momentum contribution. We note that recently [23] proved several weak versions of the Bekenstein type inequalities through studying different notions of quasi-local energy.…”

Section: Discussionmentioning

confidence: 98%

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Aspects of Quasi-local energy for gravity coupled to gauge fields

Mondal,

Yau

2022

Preprint

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We study the aspects of quasi-local energy associated with a 2−surface Σ bounding a space-like domain Ω of a physical 3+1 dimensional spacetime in the regime of gravity coupled to a gauge field. The Wang-Yau quasi-local energy together with an additional term arising due to the coupling of gravity to a gauge field constitutes the total energy (QLE) contained within the membrane Σ = ∂Ω. We specialize in the Kerr-Newman family of spacetimes which contains a U(1) gauge field coupled to gravity and an outer horizon. Through explicit calculations, we show that the total energy satisfies a weaker version of a Bekenstein type inequality QLE > Q 2 2R for large spherical membranes, Q is the charge and R is the radius of the membrane. Turning off the angular momentum (Reissner Nordström) yields QLE > Q 2 2R for all constant radii membranes containing the horizon and in such case the charge factor appearing in the right-hand side exactly equals to that of Bekenstein's inequality. Moreover, we show that the total quasi-local energy monotonically decays from 2M irr + V Q (M irr is the irreducible mass, V Q is the electric potential energy) at the outer horizon to M (M is the ADM mass) at the space-like infinity under the assumption of a small angular momentum of the black hole.

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Section: Discussionmentioning

confidence: 98%

“…A natural choice would be to consider the Wang-Yau quasi-local energy and try to establish the previous inequality. We note that recently [23] studied this inequality for several definitions of the quasi-local energy.…”

Section: Introductionmentioning

confidence: 97%

Aspects of Quasi-local energy for gravity coupled to gauge fields

Mondal,

Yau

2022

Preprint

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“…Under the new coordinate system x = (u, x 2 , x 3 ), where u is the spacetime harmonic coordinate obtained in Section 3. Let L >> 1, define the following, (1)…”

Section: Spacetime Positive Mass Theorem With Cornersmentioning

confidence: 99%

“…We would mollify the initial data set along the signed distance direction of Σ as in Section 3 of [44] (cf. Section 5 of [1]). In particular, we have the following.…”

Section: Applications Of W(σ)mentioning

confidence: 99%

On a spacetime positive mass theorem with corners

Tin-Yau¹

2021

Preprint

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In this paper we consider the positive mass theorem for general initial data sets satisfying the dominant energy condition which are singular across a piecewise smooth surface. We find jump conditions on the metric and second fundamental form which are sufficient for the positivity of the total spacetime mass. Our method extends that of [30] to the singular case (which we refer to as initial data sets with corners) using some ideas from [31]. As such we give an integral lower bound on the spacetime mass and we characterise the case of zero mass. Our approach also leads to a new notion of quasilocal mass which we show to be positive, extending the work of [54] to the spacetime case. Moreover, we give sufficient conditions under which spacetime Bartnik data sets cannot admit a fill-in satisfying the dominant energy condition. This generalises the work of [58] and [57] to the spacetime setting.

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“…There are also various localized Penrose inequalities that lower bound other quasilocal masses with the irreducible mass [85][86][87][88][89][90], and all of them can be potentially turned into such entropy bounds. However, their physical meanings are more obscure, so we do not consider them here.…”

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confidence: 99%

Outer entropy equals Bartnik-Bray inner mass and the gravitational ant conjecture

Wang

2020

Phys. Rev. D

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Entropy and energy are found to be closely tied on our quest for quantum gravity. We point out an interesting connection between the recently proposed outer entropy, a coarse-grained entropy defined for a compact spacetime domain motivated by the holographic duality, and the Bartnik-Bray quasilocal mass long known in the mathematics community. In both scenarios, one seeks an optimal spacetime fill-in of a given closed, connected, spacelike, codimension-two boundary. We show that for an outer-minimizing mean-convex surface, the Bartnik-Bray inner mass matches exactly with the irreducible mass corresponding to the outer entropy. The equivalence implies that the area laws derived from the outer entropy are mathematically equivalent as the monotonicity property of the quasilocal mass. It also gives rise to new bounds between entropy and the gravitational energy, which naturally gives the gravitational counterpart to Wall's ant conjecture. We also observe that the equality can be achieved in a conformal flow of metrics, which is structurally similar to the Ceyhan-Faulkner proof of the ant conjecture. We compute the small sphere limit of the outer entropy and it is proportional to the bulk stress tensor as one would expect for a quasilocal mass. Last, we discuss some implications of taking quantum matter into consideration in the semiclassical setting.

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Geometric Inequalities for Quasi-Local Masses

Cited by 10 publications

References 68 publications

Aspects of Quasi-local energy for gravity coupled to gauge fields

Aspects of Quasi-local energy for gravity coupled to gauge fields

On a spacetime positive mass theorem with corners

Outer entropy equals Bartnik-Bray inner mass and the gravitational ant conjecture

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