On the charged Riemannian Penrose inequality with charged matter

McCormick, Stephen

doi:10.1088/1361-6382/ab50a8

Cited by 9 publications

(11 citation statements)

References 25 publications

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“…The Riemannian case of this has also been settled. Under the assumption that the horizon is connected, this result follows from an old argument of Jang [13] when combined with the more recent development of weak inverse mean curvature flow by Huisken and Ilmanen [9] (see also [18]). The case of a disconnected horizon is more subtle when one includes electric charge and some extra care must be taken.…”

Section: Introductionmentioning

confidence: 68%

“…We are now ready to state the three versions of the charged Riemannian Penrose inequality that we require. Theorem 2.1 ( [14,18]). Let (M, g, E) be a charged asymptotically flat 3-manifold satisfying R(g) ≥ 2|E| 2 + 4|∇ • E|, containing an outermost minimal surface Σ, and assume that ∇ • E is compactly supported.…”

Section: Setup and Definitionsmentioning

confidence: 99%

“…Remark 2.1. Theorem 2.1 is essentially Theorem 1.3 of [14], after applying a minor correction, as discussed in Section 3.3 of [18]. The correction relates to the hypothesis R(g) ≥ 2|E| 2 + 4|∇ • E|, which is stronger than the usual dominant energy condition, sometimes called the enhanced dominant energy condition.…”

Section: Setup and Definitionsmentioning

confidence: 99%

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Quasi-local Penrose inequalities with electric charge

Chen

McCormick

2020

Preprint

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The Riemannian Penrose inequality is a remarkable geometric inequality between the ADM mass of an asymptotically flat manifold with non-negative 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 the mass also depends on the electric charge. In the context of quasi-local mass, one is interested in determining if, and for which quasi-local mass definitions, a quasi-local version of these inequalities also holds.It is known that the Brown-York quasi-local mass satisfies a quasi-local Riemannian Penrose inequality, however in the context of the Einstein-Maxwell equations, one expects that a quasi-local Riemannian Penrose inequality should also include a contribution from the electric charge. This article builds on ideas of Lu and Miao in [16] and of the firstnamed author in [5] to prove some charged quasi-local Penrose inequalities for a class of compact manifolds with boundary. In particular, we impose that the boundary is isometric to a closed surface in a suitable Reissner-Nordstrm manifold, which serves as a reference manifold for the quasi-local mass that we work with. In the case where the reference manifold has zero mass and non-zero electric charge, the lower bound on quasi-local mass is exactly the lower bound on the ADM mass given by the charged Riemannian Penrose inequality.

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Section: Introductionmentioning

confidence: 68%

Section: Setup and Definitionsmentioning

confidence: 99%

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Quasi-local Penrose inequalities with electric charge

Chen

McCormick

2020

Preprint

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“…This is Geroch monotonicity [32], which leads to a proof of the Penrose inequality for a single black hole. A version of the above arguments holds for the Penrose inequality with charge [43,44,48,58] using the charged Hawking mass [29].…”

Section: 2mentioning

confidence: 99%

Spacetime Harmonic Functions and Applications to Mass

Bray¹,

Hirsch²,

Kazaras³

et al. 2021

Preprint

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In the pioneering work of Stern [73], level sets of harmonic functions have been shown to be an effective tool in the study of scalar curvature in dimension 3. Generalizations of this idea, utilizing level sets of so called spacetime harmonic functions as well as other elliptic equations, are similarly effective in treating geometric inequalities involving the ADM mass. In this paper, we survey recent results in this context, focusing on applications of spacetime harmonic functions to the asymptotically flat and asymptotically hyperbolic versions of the spacetime positive mass theorem, and additionally introduce a new concept of total mass valid in both settings which is encoded in interpolation regions between generic initial data and model geometries. Furthermore, a novel and elementary proof of the positive mass theorem with charge is presented, and the level set approach to the Penrose inequality given by Huisken and Ilmanen is related to the current developments. Lastly, we discuss several open problems.

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“…Furthermore, results are typically stated within the framework of initial data sets for the Einstein equations that satisfy the relevant energy condition, and the inclusion of angular momentum/charge requires the absence of angular momentum/charge density outside the horizon in addition to axisymmetry (which is only needed for angular momentum). The Penrose inequality has been established in the case of maximal data by Bray [8] and Huisken-Ilmanen [34], and charge was added in [40,44]. The inclusion of angular momentum is much more difficult and has not yet been established, although see [3,38] for partial results.…”

Section: Introductionmentioning

confidence: 99%

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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On the charged Riemannian Penrose inequality with charged matter

Cited by 9 publications

References 25 publications

Quasi-local Penrose inequalities with electric charge

Quasi-local Penrose inequalities with electric charge

Spacetime Harmonic Functions and Applications to Mass

Geometric Inequalities for Quasi-Local Masses

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