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On Penrose inequality in holography
High Energy Physics - Theory · Submitted 26 Apr 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In this case, the holographic argument implies that the Penrose inequality should still be valid but this paper use concrete example to show that whether the Penrose inequality holds or not will depend on what kind of quantization scheme we employ.
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The abstract, sentence by sentence
The recent holographic deduction of Penrose inequality only assumes null energy condition while the weak or dominant energy condition is required in usual geometric proof. This paper makes a step toward filling up gap between these two approaches. For planar/spherically symmetrically asymptotically Schwarzschild anti-de Sitter (AdS) black holes, we give a purely geometric proof for Penrose inequality by assuming the null energy condition. We also point out that two naive generalizations of charged Penrose inequality are not generally true and propose two new candidates. When the spacetime is asymptotically AdS but not Schwarzschild-AdS, the total mass is defined according to holographic renormalization and depends on scheme of quantization. In this case, the holographic argument implies that the Penrose inequality should still be valid but this paper use concrete example to show that whether the Penrose inequality holds or not will depend on what kind of quantization scheme we employ.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The recent holographic deduction of Penrose inequality only assumes null energy condition while the weak or dominant energy condition is required in usual geometric proof. | background 0.97 | 0.08 | 0.09 | asserted 1.00 |
| s1 | This paper makes a step toward filling up gap between these two approaches. | contribution 0.49 | 0.52 | 0.05 | asserted 0.91 |
| s2 | For planar/spherically symmetrically asymptotically Schwarzschild anti-de Sitter (AdS) black holes, we give a purely geometric proof for Penrose inequality by assuming the null energy condition. | contribution 0.81 | 0.96 | 0.63 | asserted 1.00 |
| s3 | We also point out that two naive generalizations of charged Penrose inequality are not generally true and propose two new candidates. | result 0.72 | 0.94 | 0.15 | asserted 1.00 |
| s4 | When the spacetime is asymptotically AdS but not Schwarzschild-AdS, the total mass is defined according to holographic renormalization and depends on scheme of quantization. | background 0.88 | 0.17 | 0.06 | asserted 1.00 |
| s5 | In this case, the holographic argument implies that the Penrose inequality should still be valid but this paper use concrete example to show that whether the Penrose inequality holds or not will depend on what kind of quantization scheme we employ. | result 0.94 | 0.89 | 0.35 | asserted 0.93 |
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The paper
Original abstract
The recent holographic deduction of Penrose inequality only assumes null energy condition while the weak or dominant energy condition is required in usual geometric proof. This paper makes a step toward filling up gap between these two approaches. For planar/spherically symmetrically asymptotically Schwarzschild anti-de Sitter (AdS) black holes, we give a purely geometric proof for Penrose inequality by assuming the null energy condition. We also point out that two naive generalizations of charged Penrose inequality are not generally true and propose two new candidates. When the spacetime is asymptotically AdS but not Schwarzschild-AdS, the total mass is defined according to holographic renormalization and depends on scheme of quantization. In this case, the holographic argument implies that the Penrose inequality should still be valid but this paper use concrete example to show that whether the Penrose inequality holds or not will depend on what kind of quantization scheme we employ.
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References
How the literature uses it
3 arXiv papers cite this in 6 sentences
Papers citing it · 5 sentences without a confident label
Cites it as background 1 paper
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The fourth quasi-local mass was recently proposed in Refs. [ref] .
Tightening the Penrose Inequality · Quasi-local masses and proof of inequality · 0.87
What it cites · 33 sentences without a confident label
Contests 4 papers
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This implies that the conclusions of Refs. [ref] implicitly depend on the topology of event horizon, though more detailed reason is still unclear for us.
Microcanonical Path Integrals and the Holography of small Black Hole Interiors · Introduction · contest 0.78
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This implies that the conclusions of Refs. [ref] implicitly depend on the topology of event horizon, though more detailed reason is still unclear for us.
A Holographic Argument for the Penrose Inequality in AdS · Introduction · contest 0.78
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However, there are also counterexamples [ref] for such charged generalization [ref].
Stability analysis on charged black hole with non-linear complex scalar · Introduction · contest 0.74
Uses the method or tool of 6 papers
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This paper follows the standard holographic renormalization procedure [ref] and obtain the holographic mass as the total mass.
Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence · Introduction · 1.00
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This paper follows the standard holographic renormalization procedure [ref] and obtain the holographic mass as the total mass.
Lecture Notes on Holographic Renormalization · Introduction · 1.00
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Following standard holographic renormalization scheme [ref] , the counter term for gravitational sector in this case is given by [equation] Since mass satisfying $-d^2/4<m^2<1-d^2/4$, there are two different renormalization schemes [ref] for scalar field $ϕ(r )$ sector.
Boundary Conditions and Dualities: Vector Fields in AdS/CFT · Numerical check on Penrose inequality · 0.88
Compares with 1 paper
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This one is very similar to the generalization proposed by Ref. [ref] , however, $Q_m$ here in general will be different from the total charge.
Penrose Inequality for Asymptotically AdS Spaces · The First Type of Generalization · 1.00
Cites as support 3 papers
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Moreover, given same total mass $M$, Ref. [ref] shows via holography that boundary's QFT state dual to Schwarzschild-AdS black hole has the maximum entropy.
Microcanonical Path Integrals and the Holography of small Black Hole Interiors · Introduction · 0.98
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See Refs. [ref] for a counterexample.
On the charged Riemannian Penrose inequality with charged matter · Charged Black Holes · 0.97
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See Refs. [ref] for a counterexample.
Stability analysis on charged black hole with non-linear complex scalar · Charged Black Holes · 0.97
Cites as background 5 papers
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In holography, the bulk's geometry is dual to the two asymptotically boundary's QFT state [ref] .
Anti De Sitter Space And Holography · Introduction · 0.98
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In holography, the bulk's geometry is dual to the two asymptotically boundary's QFT state [ref] .
Large N Field Theories, String Theory and Gravity · Introduction · 0.98
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In general relativity, there are many famous and universal inequalities, such as the Penrose inequality [ref] , the positive mass theorem [ref] , the second law of black holes [ref] and so on.
The Thermodynamics of Black Holes · Introduction · 1.00
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