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Geometric Constraints via Page Curves: Insights from Island Rule and Quantum Focusing Conjecture

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arxiv 2405.03220 v2 pith:VTFT255N submitted 2024-05-06 hep-th gr-qc

Ming-Hui Yu , Xian-Hui Ge This is my paper · ORCID
classification hep-thgr-qc
keywords pagecurvefocusingislandblackconjecturecurvesgeometric
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abstract

Exploring the inverse problem tied to the Page curve phenomenon and island paradigm, we investigate the geometric conditions underpinning black hole evaporation where information is preserved and islands manifest, giving rise to the characteristic Page curve. Focusing on a broad class of static black hole metrics in asymptotically Minkowski or (anti-)de Sitter spacetimes, we derive a pivotal constraint on the blacken factor $f(r)$ for which the island exists and reproduce the Page curve. Specifically, we reveal that a sufficient yet not universally necessary criterion -- manifested in the negativity of the second derivative of $f(r)$, i.e. $f^{\prime \prime} (r)<0$, in proximity to the event horizon where $r \sim r_h+ {\cal O} (G_N)$, ensures the emergence of Page curves in a manner transcending specific theoretical models. This pivotal finding, supported by the tenets of the quantum focusing conjecture.

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Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. New insights on mutual information in the island approach to the Page curve

    hep-th 2026-07 conditional novelty 5.0 of 10

    At scrambling time I(B+:B−)=0 forces I(I:R)→∞, interpreted as conservation of geometric correlation, while I(I:R+:R−) is shown always negative via Cauchy-slice identities.

  2. Island rules for the noncommutative black hole

    hep-th 2025-05 conditional novelty 5.0 of 10

    For noncommutative black holes, including quantum islands in the radiation entropy reproduces the Page curve and pushes the Page time far later than for Schwarzschild black holes.

  3. Island of acoustic black hole in Schwarzschild spacetime

    hep-th 2025-12 conditional novelty 4.0 of 10

    For a Schwarzschild-surrounded acoustic black hole, phonon entanglement entropy follows a Page curve in the non-extremal case but diverges (no Page time) in the extremal case, according to the island formula.

  4. Replica Wormholes, Modular Entropy, and Capacity of Entanglement in JT Gravity

    hep-th 2025-01 conditional novelty 4.0 of 10

    In JT gravity toy models, late-time modular entropy and capacity of entanglement scale inversely with n times the inverse temperature, supporting a thermal reading of the replica parameter.

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