A quasi-local Penrose inequality for the quasi-local energy with static references

Chen, Po‐Ning

doi:10.1090/tran/8158

Cited by 2 publications

(1 citation statement)

References 32 publications

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“…As in Section 7 this proof may be parlayed into versions of Theorems 2.12 and 2.13 for the static Wang-Yau mass. In addition, we note that the same methods can be used to generalize the result of P.-N. Chen [11], concerning Brown-York mass with general spherically symmetric static reference, to the setting of static Liu-Yau mass.…”

Section: Penrose-like Inequality For Quasi-local Mass With a Static Rmentioning

confidence: 89%

Geometric Inequalities for Quasi-Local Masses

Alaee

Khuri

Yau

2020

Commun. Math. Phys.

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In this paper lower bounds are obtained for quasi-local masses in terms of charge, angular momentum, and horizon area. In particular we treat three quasi-local masses based on a Hamiltonian approach, namely the Brown-York, Liu-Yau, and Wang-Yau masses. The geometric inequalities are motivated by analogous results for the ADM mass. They may be interpreted as localized versions of these inequalities, and are also closely tied to the conjectured Bekenstein bounds for entropy of macroscopic bodies. In addition, we give a new proof of the positivity property for the Wang-Yau mass which is used to remove the spin condition in higher dimensions. Furthermore, we generalize a recent result of Lu and Miao to obtain a localized version of the Penrose inequality for the static Wang-Yau mass.

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Section: Penrose-like Inequality For Quasi-local Mass With a Static Rmentioning

confidence: 89%

Geometric Inequalities for Quasi-Local Masses

Alaee

Khuri

Yau

2020

Commun. Math. Phys.

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Quasi-Local Penrose Inequalities with Electric Charge

Chen

McCormick

2021

International Mathematics Research Notices

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The Riemannian Penrose inequality is a remarkable geometric inequality between the ADM mass of an asymptotically flat manifold with nonnegative scalar curvature and the area of its outermost minimal surface. A version of the Riemannian Penrose inequality has also been established for the Einstein–Maxwell equations where the lower bound on mass depends also on electric charge, a charged Riemannian Penrose inequality. Here, we establish some quasi-local charged Penrose inequalities for surfaces isometric to closed surfaces in a suitable Reissner–Nordström manifold, which serves as a reference manifold for the quasi-local mass. In the case where the reference manifold has zero mass and nonzero electric charge, the lower bound on quasi-local mass is exactly the lower bound on the ADM mass given by the charged Penrose inequality.

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A quasi-local Penrose inequality for the quasi-local energy with static references

Cited by 2 publications

References 32 publications

Geometric Inequalities for Quasi-Local Masses

Geometric Inequalities for Quasi-Local Masses

Quasi-Local Penrose Inequalities with Electric Charge

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