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Covariant Holographic Entropy Cone
Authors:
Bowen Zhao
Abstract:
The holographic entropy cone classifies the possible entanglement structures of quantum states with a classical gravity dual. For static geometries, Bao et al. established that this cone is polyhedral by constructing a graph model from Ryu-Takayanagi (RT) surfaces on a time-symmetric slice. Extending this framework to general, time-dependent states governed by the Hubeny-Rangamani-Takayanagi (HRT)…
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The holographic entropy cone classifies the possible entanglement structures of quantum states with a classical gravity dual. For static geometries, Bao et al. established that this cone is polyhedral by constructing a graph model from Ryu-Takayanagi (RT) surfaces on a time-symmetric slice. Extending this framework to general, time-dependent states governed by the Hubeny-Rangamani-Takayanagi (HRT) formula has remained an open problem, as the relevant extremal surfaces do not lie on a common spatial slice. We resolve this by constructing a graph model directly from the causal structure of entanglement wedges. By proving a key "no-short-cut" theorem, we show that minimization over graph cuts reduces to a consideration of cuts corresponding to unions of complete HRT surfaces, establishing the equivalence of the covariant and static holographic entropy cones. Consequently, all foundational results, including polyhedrality and the finite nature of entropy inequalities, extend to general holographic states.
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Submitted 25 January, 2026;
originally announced February 2026.
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Beyond $2$-to-$2$: Geometrization of Entanglement Wedge Connectivity in Holographic Scattering
Authors:
Bowen Zhao
Abstract:
We extend recent discussions on generalization of the Connected Wedge Theorem about $2$-to-$2$ holographic scattering problem to $n$-to-$n$ scatterings ($n>2$). In this broader setting, our theorem provides a weaker necessary condition for the connectedness of boundary entanglement wedges than previously identified. Besides, we prove a novel sufficient condition for this connectedness. We also pre…
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We extend recent discussions on generalization of the Connected Wedge Theorem about $2$-to-$2$ holographic scattering problem to $n$-to-$n$ scatterings ($n>2$). In this broader setting, our theorem provides a weaker necessary condition for the connectedness of boundary entanglement wedges than previously identified. Besides, we prove a novel sufficient condition for this connectedness. We also present an analysis of the criteria ensuring a non-empty entanglement wedge intersection region $\mathcal{S}_E$. These results refine the holographic dictionary between geometric connectivity and quantum entanglement for general multi-particle scattering.
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Submitted 22 January, 2026; v1 submitted 7 December, 2025;
originally announced December 2025.
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Enhanced energy extraction via magnetic reconnection in Kerr-AdS spacetime
Authors:
Bo Zhao,
Chao-Hui Wang,
Shao-Wen Wei
Abstract:
In this paper, we study the energy extraction from Kerr-AdS black holes following the magnetic reconnection process. The parameter space regions that satisfy the energy extraction condition, as well as the efficiency and power of the extracted energy, are analyzed. The study shows that the presence of a negative cosmological constant extends the range of dominant reconnection radial locations wher…
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In this paper, we study the energy extraction from Kerr-AdS black holes following the magnetic reconnection process. The parameter space regions that satisfy the energy extraction condition, as well as the efficiency and power of the extracted energy, are analyzed. The study shows that the presence of a negative cosmological constant extends the range of dominant reconnection radial locations where the energy extraction condition is met, and enables energy extraction even from black holes with relatively low spin. Furthermore, the influence of the negative cosmological constant on energy extraction is modulated by the extent of the dominant reconnection radial region: a more negative cosmological constant enhances the extracted energy, efficiency, and power, particularly for smaller dominant reconnection radii. These results demonstrate that the energy extraction from Kerr-AdS black holes is more favorable than that from their asymptotically flat counterparts. Our results highlight the crucial role of the cosmological constant in energy extraction via magnetic reconnection.
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Submitted 27 November, 2025;
originally announced December 2025.
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A proof of Generalized Connected Wedge Theorem
Authors:
Bowen Zhao
Abstract:
In the context of asymptotic $2$-to-$2$ scattering process in AdS/CFT, the Connected Wedge Theorem identifies the existence of $O(1/G_N)$ mutual information between suitable boundary subregions, referred to as decision regions, as a necessary but not sufficient condition for bulk-only scattering processes, i.e., nonempty bulk scattering region $S_0$. Recently, Liu and Leutheusser proposed an enlar…
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In the context of asymptotic $2$-to-$2$ scattering process in AdS/CFT, the Connected Wedge Theorem identifies the existence of $O(1/G_N)$ mutual information between suitable boundary subregions, referred to as decision regions, as a necessary but not sufficient condition for bulk-only scattering processes, i.e., nonempty bulk scattering region $S_0$. Recently, Liu and Leutheusser proposed an enlarged bulk scattering region $S_E$ and conjectured that the non-emptiness of $S_E$ fully characterizes the existence of $O(1/G_N)$ mutual information between decision regions. Here, we provide a geometrical or general relativity proof for a slightly modified version of their conjecture.
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Submitted 7 December, 2025; v1 submitted 27 September, 2025;
originally announced September 2025.
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A proposal of quasi-local mass for 2-surfaces of timelike mean curvature
Authors:
Bowen Zhao,
Shing-Tung Yau,
Lars Andersson
Abstract:
A quasi-local mass, typically defined as an integral over a spacelike $2$-surface $Σ$, should encode information about the gravitational field within a finite, extended region bounded by $Σ$. Therefore, in attempts to quantize gravity, one may consider an infinite dimensional space of $2$-surfaces instead of an infinite dimensional space of $4$-dimensional Lorentzian spacetimes. However, existing…
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A quasi-local mass, typically defined as an integral over a spacelike $2$-surface $Σ$, should encode information about the gravitational field within a finite, extended region bounded by $Σ$. Therefore, in attempts to quantize gravity, one may consider an infinite dimensional space of $2$-surfaces instead of an infinite dimensional space of $4$-dimensional Lorentzian spacetimes. However, existing definitions for quasilocal mass only applies to surfaces outside an horizon whose mean curvature vector is spacelike. In this paper, we propose an extension of the Wang-Yau quasi-local energy/mass to surfaces with timelike mean curvature vector, including in particular trapped surfaces. We adopt the same canonical gauge as in the Wang-Yau quasi-local energy but allow the pulled back "killing vector" to the physical spacetime to be spacelike. We define the new quasi-local energy along the Hamiltonian formulation of the Wang-Yau quasi-local energy. The new definition yields a positive definite surface energy density and a new divergence free current. Calculations for coordinate spheres in Kerr family spacetime are shown. In the spherical symmetric case, our definition reduces to a previous definition \cite{lundgren2007self}.
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Submitted 30 June, 2024;
originally announced July 2024.
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Strong field behavior of Wang-Yau Quasi-local energy
Authors:
Bowen Zhao,
Lars Andersson,
Shing-Tung Yau
Abstract:
We look at the strong field behavior of the Wang-Yau quasi-local energy. In particular, we examine the limit of the Wang-Yau quasi-local energy as the defining spacelike $2$-surface $Σ$ approaches an apparent horizon from outside. Assuming that coordinate functions of the isometric embedding are bounded in $W^{2,1}$ and mean curvature vector of the image surface remains spacelike, we find that the…
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We look at the strong field behavior of the Wang-Yau quasi-local energy. In particular, we examine the limit of the Wang-Yau quasi-local energy as the defining spacelike $2$-surface $Σ$ approaches an apparent horizon from outside. Assuming that coordinate functions of the isometric embedding are bounded in $W^{2,1}$ and mean curvature vector of the image surface remains spacelike, we find that the limit falls in two exclusive cases: 1) If the horizon cannot be isometrically embedded into $R^3$, the Wang-Yau quasi-local energy blows up as $Σ$ approaches the horizon while the optimal embedding equation is not solvable for $Σ$ near the horizon; 2) If the horizon can be isometrically embedded into $R^3$, the optimal embedding equation is solvable up to the horizon with the unique solution at the horizon corresponding to isometric embedding into $R^3$ and the Wang-Yau quasi-local mass admits a finite limit at the horizon. We discuss the implications of our results in the conclusion section.
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Submitted 15 October, 2024; v1 submitted 15 June, 2024;
originally announced June 2024.
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Some Remarks on Wang-Yau Quasi-Local Mass
Authors:
Bowen Zhao,
Lars Andersson,
Shing-Tung Yau
Abstract:
We review Wang-Yau quasi-local definitions along the line of gravitational Hamiltonian. This makes clear the connection and difference between Wang-Yau definition and Brown-York or even global ADM definition. We make a brief comment on admissibility condition in Wang-Yau quasi-lcoal mass. We extend the positivity proof for Wang-Yau quasi-local energy to allow possible presence of strictly stable a…
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We review Wang-Yau quasi-local definitions along the line of gravitational Hamiltonian. This makes clear the connection and difference between Wang-Yau definition and Brown-York or even global ADM definition. We make a brief comment on admissibility condition in Wang-Yau quasi-lcoal mass. We extend the positivity proof for Wang-Yau quasi-local energy to allow possible presence of strictly stable apparent horizons through establishing solvability of Dirac equation in certain 3-manifolds that possess cylindrical ends, as in the case of Jang's graph blowing up at marginally outer trapped surfaces.
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Submitted 29 February, 2024;
originally announced February 2024.
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Stringent Tests of Lorentz Invariance Violation from LHAASO Observations of GRB 221009A
Authors:
The LHAASO Collaboration,
Zhen Cao,
F. Aharonian,
Axikegu,
Y. X. Bai,
Y. W. Bao,
D. Bastieri,
X. J. Bi,
Y. J. Bi,
W. Bian,
A. V. Bukevich,
Q. Cao,
W. Y. Cao,
Zhe Cao,
J. Chang,
J. F. Chang,
A. M. Chen,
E. S. Chen,
H. X. Chen,
Liang Chen,
Lin Chen,
Long Chen,
M. J. Chen,
M. L. Chen,
Q. H. Chen
, et al. (261 additional authors not shown)
Abstract:
On October 9, 2022, the Large High Altitude Air Shower Observatory (LHAASO) reported the observation of the very early TeV afterglow of the brightest-of-all-time GRB 221009A, recording the highest photon statistics in the TeV band ever from a gamma-ray burst. We use this unique observation to place stringent constraints on an energy dependence of the speed of light in vacuum, a manifestation of Lo…
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On October 9, 2022, the Large High Altitude Air Shower Observatory (LHAASO) reported the observation of the very early TeV afterglow of the brightest-of-all-time GRB 221009A, recording the highest photon statistics in the TeV band ever from a gamma-ray burst. We use this unique observation to place stringent constraints on an energy dependence of the speed of light in vacuum, a manifestation of Lorentz invariance violation (LIV) predicted by some quantum gravity (QG) theories. Our results show that the 95% confidence level lower limits on the QG energy scales are $E_{\mathrm{QG},1}>10$ times of the Planck energy $E_\mathrm{Pl}$ for the linear, and $E_{\mathrm{QG},2}>6\times10^{-8}E_\mathrm{Pl}$ for the quadratic LIV effects, respectively. Our limits on the quadratic LIV case improve previous best bounds by factors of 5--7.
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Submitted 13 February, 2026; v1 submitted 8 February, 2024;
originally announced February 2024.
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Properties of Quasi-local mass in binary black hole mergers
Authors:
Daniel Pook-Kolb,
Bowen Zhao,
Lars Andersson,
Badri Krishnan,
Shing-Tung Yau
Abstract:
Identifying a general quasi-local notion of energy-momentum and angular momentum would be an important advance in general relativity with potentially important consequences for mathematical and astrophysical studies in general relativity. In this paper we study a promising approach to this problem first proposed by Wang and Yau in 2009 based on isometric embeddings of closed surfaces in Minkowski…
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Identifying a general quasi-local notion of energy-momentum and angular momentum would be an important advance in general relativity with potentially important consequences for mathematical and astrophysical studies in general relativity. In this paper we study a promising approach to this problem first proposed by Wang and Yau in 2009 based on isometric embeddings of closed surfaces in Minkowski space. We study the properties of the Wang-Yau quasi-local mass in high accuracy numerical simulations of the head-on collisions of two non-spinning black holes within full general relativity. We discuss the behavior of the Wang-Yau quasi-local mass on constant expansion surfaces and we compare its behavior with the irreducible mass. We investigate the time evolution of the Wang-Yau Quasi-local mass in numerical examples. In addition we discuss mathematical subtleties in defining the Wang-Yau mass for marginally trapped surfaces.
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Submitted 19 August, 2023;
originally announced August 2023.
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Constraining Light Scalar Field with Torsion-Balance Gravity Experiments
Authors:
ChengGang Qin,
XiaoYu Lu,
BingChen Zhao,
Jun Ke,
AnBin Du,
Jie Luo,
YuJie Tan,
ChengGang Shao
Abstract:
The light scalar field with a coupling to standard model particles provide a possible source of the dark matter, long-range Yukawa forces or violation of the weak equivalence principle, which can be potentially explored by precision gravity experiments. We describe the searches for such light scalar fields with the three types of gravity experiments, including the $G$-measurement experiments, Inve…
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The light scalar field with a coupling to standard model particles provide a possible source of the dark matter, long-range Yukawa forces or violation of the weak equivalence principle, which can be potentially explored by precision gravity experiments. We describe the searches for such light scalar fields with the three types of gravity experiments, including the $G$-measurement experiments, Inverse-Square Law (ISL) experiments, and equivalence principle experiments. We investigate the potential influences of the scalar field as a function of its mass, and focus on the experimental constraints from torsion-balance gravity experiments. HUST-18 $G$-measurement torsion-balance experiments place bounds on the photon coupling and electron coupling at up to $Λ_γ=7\times10^{17}$ GeV and $Λ_{e}=1\times10^{17}$ GeV in the mass ranges $10^{-9}-10^{-4}$ eV. Results from the ISL experiments by the Universities of Washington, Stanford, IUPUI, HUST, Colorado, Irvine, Yale and others allow us to set limits on the photon coupling and electron coupling at up to $Λ_γ=5\times10^{17}$ GeV and $Λ_{e}=3\times10^{16}$ GeV for scalar field mass ranges between $10^{-5}$ and $10^{-1}$ eV. Additionally, we also discuss the limits from equivalence principle experiments, and $MICROSCOPE$ final result updates the constrains on the coupling parameters at up to $Λ_γ=7\times10^{22}$ GeV and $Λ_{e}=4\times10^{21}$ GeV for mass ranges $\lesssim 10^{-13}$ eV. These results contribute experimental constraints to relatively unexplored mass regions of {light scalar field} parameter space and improve upon previous limits in some mass ranges. This work paves the way for long-range Yukawa forces mediated by light scalar fields in future high-precision gravity experiments.
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Submitted 3 March, 2024; v1 submitted 12 December, 2022;
originally announced December 2022.