The small sphere limit of quasilocal energy in higher dimensions along lightcone cuts

Wang, Jinzhao

doi:10.1088/1361-6382/ab719d

Cited by 6 publications

(7 citation statements)

References 37 publications

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“…) which is exactly the result we expect from volume Ω n−2 n−1 times the matter energy density T (e 0 , e 0 )| p . It matches with the non-vacuum small sphere limits of other quasilocal masses in four dimensions [18] and higher dimensions [97]. Note that this result holds for both the AF case (4.6) and the AH case (4.7), because the second term with higher power in (4.7) is irrelevant at the leading order.…”

Section: The Gravitational Ant Conjecturesupporting

confidence: 80%

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

Wang

2020

Preprint

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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. Lastly, we discuss some implications of taking quantum matter into consideration in the semiclassical setting.

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Section: The Gravitational Ant Conjecturesupporting

confidence: 80%

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

Wang

2020

Preprint

Self Cite

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show abstract

“…which is exactly the result we expect from volume Ω n−2 n−1 times the matter energy density Tðe 0 ; e 0 Þj p . It matches with the nonvacuum small sphere limits of other quasilocal masses in four dimensions [18] and higher dimensions [96]. Note that this result holds for both the AF case (14) and the AH case (15), because the second term with higher power in (15) is irrelevant at the leading order.…”

Section: Application: the Small Sphere Limitsupporting

confidence: 78%

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

Wang

2020

Phys. Rev. D

Self Cite

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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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“…Indeed, as reviewed in a moment, the Bartnik mass does not fail to meet this natural expectation, and the present article is motivated by a desire to identify the next most significant contributions. See for example [15,19,20,27,31,52,53,57] for estimates of other quasilocal masses of small spheres in both Riemannian and spacetime settings.…”

Section: Motivation and Statement Of The Resultsmentioning

confidence: 99%

Second-order mass estimates for static vacuum metrics with small Bartnik data

Wiygul¹

2021

Preprint

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Given on the 2-sphere Bartnik data (prescribed metric and mean curvature) that is a small perturbation of the corresponding data for the standard unit sphere in Euclidean space, we estimate to second order, in the size of the perturbation, the mass of the asymptotically flat static vacuum extension (unique up to diffeomorphism) which is a small perturbation of the flat metric on the exterior of the unit ball in Euclidean space and induces the prescribed data on the boundary sphere. As an application we obtain a new upper bound on the Bartnik mass of small metric spheres to fifth order in the radius.

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The small sphere limit of quasilocal energy in higher dimensions along lightcone cuts

Cited by 6 publications

References 37 publications

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

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

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

Second-order mass estimates for static vacuum metrics with small Bartnik data

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