The DOI matches its Crossref record; 251 of the 251 references it cites were found in a registry or an index.
Time dependence of Hawking radiation entropy
Open accessAbstract
If a black hole starts in a pure quantum state and evaporates completely by a unitary process, the von Neumann entropy of the Hawking radiation initially increases and then decreases back to zero when the black hole has disappeared. Here numerical results are given for an approximation to the time dependence of the radiation entropy under an assumption of fast scrambling, for large nonrotating black holes that emit essentially only photons and gravitons. The maximum of the von Neumann entropy then occurs after about 53.81% of the evaporation time, when the black hole has lost about 40.25% of its original Bekenstein-Hawking (BH) entropy (an upper bound for its von Neumann entropy) and then has a BH entropy that equals the entropy in the radiation, which is about 59.75% of the original BH entropy 4π M 0 2 , or about 7.509 M 0 2 ≈ 6.268 × 10 76 ( M 0 / M ⊙ ) 2 , using my 1976 calculations that the photon and graviton emission process into empty space gives about 1.4847 times the BH entropy loss of the black hole. Results are also given for black holes in initially impure states. If the black hole starts in a maximally mixed state, the von Neumann entropy of the Hawking radiation increases from zero up to a maximum of about 119.51% of the original BH entropy, or about 15.018 M 0 2 ≈ 1.254 × 10 77 ( M 0 / M ⊙ ) 2 , and then decreases back down to 4π M 0 2 = 1.049 × 10 77 ( M 0 / M ⊙ ) 2 .
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The cited source doesn’t support the claim as written.
In the citing paper
“For black holes in our universe, both events occur when the black hole has approximately 90% evaporated [7].”
From Entanglement wedge reconstruction and the information paradox (2020) · cites this paper as [7]
Checked by a reasoning model — may be wrong.
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“The factor of two in (3.3) arises because the Hawking radiation is not adiabatic and it generates coarse grained entropy [4] (see also [8]).”
From The Page curve of Hawking radiation from semiclassical geometry (2020) · cites this paper as [4]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“The inclusion of this spatially disconnected island leads to reproduction the Page curve [47,48] for the timedependence of the von Neumann entropy of the Hawking radiation in consistency with unitarity without invalidating the effective semiclassical description of bulk”
From Holographic spacetime, black holes and quantum error correcting codes: a review (2022) · cites this paper as [48]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“This is a consequence of Page's theorem [47,48] which states that for a typical pure state in a bipartite system with one system being much smaller than the other, the trace distance between the density matrix of the smaller subsystem and the microcanonical ensemble is of the order of e -S/2 with S being the number of qubits in the larger one.”
From Holographic spacetime, black holes and quantum error correcting codes: a review (2022) · cites this paper as [48]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“But if the evaporation is unitary, then it must eventually fall back to zero following the Page curve [2, 3].”
From Replica wormholes and the entropy of Hawking radiation (2020) · cites this paper as [3]
Experimental — accuracy not yet measured
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Despite its simplicity, this setup exhibits Hawking's information paradox, and the corresponding puzzle with the Page curve [2, 3].”
From Replica wormholes and the entropy of Hawking radiation (2020) · cites this paper as [3]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“Using this we compute the entropy of Hawking radiation and argue that it follows the Page curve, as suggested by recent computations of the entropy and entanglement wedges for old black holes.”
From The Page curve of Hawking radiation from semiclassical geometry (2020) · cites this paper as [4]
The cited source says what the claim attributes to it.
In the citing paper
“This means that the Page time, which we recall is defined by S rad = A hor 4G N , (2.4) occurs when the horizon area A hor > A 0 hor /2, despite commonly being called the halfway point of the evaporation [7].”
From Entanglement wedge reconstruction and the information paradox (2020) · cites this paper as [7]
The cited source says what the claim attributes to it.
In the citing paper
“The Page time is commonly called the 'halfway point' in the black hole evaporation, although, because of the thermodynamic irreversibility of the evaporation and the time dependence of the black hole temperature, it does not occur halfway through the evaporation either by time or by horizon area/entropy[7].”
From Entanglement wedge reconstruction and the information paradox (2020) · cites this paper as [7]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Particle creation by black holes
Hawking, S. W. (1975) · Communications In Mathematical Physics · doi:10.1007/bf02345020 · Cited by 13,106 · cited 3×
“A central question concerns the entanglement of a black hole with the Hawking radiation [184, 185] that has been emitted.”
BackgroundBekenstein, J. D. (1973) · Physical Review D · doi:10.1103/physrevd.7.2333 · Cited by 7,555
Beringer, J., Arguin, J.-F., Barnett, R. M., Copic, K., Dahl, O. I., Groom, D. E., Lin, C.-J., Lys, J., Murayama, H., Wohl, C. G., et al. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.86.010001 · Cited by 5,996
HAWKING, S. W. (1974) · Nature · doi:10.1038/248030a0 · Cited by 5,669 · cited 2×
“The semiclassical approximation for the black hole emission [1, 185, 186] would then give the time-dependence of the coarse-grained entropy of a decaying large nonrotating uncharged black hole and of the emitted radiation as”
Breakdown of predictability in gravitational collapse
Hawking, S. W. (1976) · Physical Review D · doi:10.1103/physrevd.14.2460 · Cited by 2,554
Particle creation by black holes
Hawking, S. W. (1976) · Communications in Mathematical Physics · doi:10.1007/bf01608497 · Cited by 1,873
Srednicki, M. (1993) · Physical Review Letters · doi:10.1103/physrevlett.71.666 · Cited by 1,858
Average entropy of a subsystem
Page, D. N. (1993) · Physical Review Letters · doi:10.1103/physrevlett.71.1291 · Cited by 1,578
Self-citationEternal black holes in anti-de Sitter
Maldacena, J. (2003) · Journal of High Energy Physics · doi:10.1088/1126-6708/2003/04/021 · Cited by 1,555
Black holes and the second law
Bekenstein, J. D. (1972) · Lettere Al Nuovo Cimento Series 2 · doi:10.1007/bf02757029 · Cited by 1,485
Research works printed but not linked: 5
- D.N. Page, 1982, Proc. Gen. Rel. Part B, 1153
- J.A. Harvey, 1992, Proc. String Theor. Quant. Grav., 122
- F. Wilczek, 1993, Proc. Black holes, membranes, wormholes and superstrings, 19 pg. 306377
- D.N. Page, 1994, Proc. of the 5th Canadian Conference on General Relativity and Relativistic Astrophysics, pg. 1
- D. Ahn, 2007, J. High Energy Phys., 2007, 021
Cited by
Sorted by citations
Items 201–300 of 355
Quantum focusing conjecture and the Page curve
Matsuo, Y. (2023) · Journal of High Energy Physics · doi:10.1007/jhep12(2023)050 · Cited by 7
Concerns about the replica wormhole derivation of the island conjecturePreprint
Karlsson, A. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2101.05879 · Cited by 6
Hybrid quantum states in 2D dilaton gravity
Potaux, Y., Sarkar, D., & Solodukhin, S. N. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.125012 · Cited by 9
Entanglement negativity and defect extremal surface
Shao, Y., Yuan, M.-K., & Zhou, Y. (2024) · SciPost Physics Core · doi:10.21468/scipostphyscore.7.2.027 · Cited by 14
Entanglement inside a black hole before the Page time
Liu, Y., Jian, S.-K., Ling, Y., & Xian, Z.-Y. (2024) · Journal of High Energy Physics · doi:10.1007/jhep07(2024)043 · Cited by 6
The D-dimensional charged AdS black holes solutions in polytropic dark energy from Barrow entropy
Sekhmani, Y., Hazarika, B., Phukon, P., Landry, A., Maurya, S. K., & Rayimbaev, J. (2025) · The European Physical Journal C · doi:10.1140/epjc/s10052-025-14344-1 · Cited by 5
Modifications of the Page Curve from correlations within Hawking radiation
Alvi, M. A., Majumdar, M. A., Matin, M. A., Rahat, M. H., & Roy, A. (2019) · Physics Letters B · doi:10.1016/j.physletb.2019.134881 · Cited by 5
Kibe, T., Mondkar, S., Mukhopadhyay, A., & Swain, H. (2023) · Journal of High Energy Physics · doi:10.1007/jhep10(2023)096 · Cited by 7
Kumar, K., & Marto, J. (2024) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptae176 · Cited by 5
Hawking radiation with pure states
Kumar, K. S., & Marto, J. (2024) · General Relativity and Gravitation · doi:10.1007/s10714-024-03329-2 · Cited by 5
Black hole tunneling in loop quantum gravity*
Tan, H., Guo, R.-Z., & Zhang, J. (2025) · Chinese Physics C · doi:10.1088/1674-1137/adabd0 · Cited by 5
The black hole information paradox and highly squeezed interior quantum fluctuations
Oshita, N. (2017) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aa84e3 · Cited by 5
Thermodynamic properties of modified hairy and BTZ black holes
Muhammad, Y., Bamba, K., & Jawad, A. (2021) · International Journal of Modern Physics D · doi:10.1142/s0218271821500681 · Cited by 5
Marto, J. (2021) · Universe · doi:10.3390/universe7080297 · Cited by 6
Page Curves and Islands in Charged Dilaton Black HolesPreprint
Yu, M., & Ge, X.-H. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2107.03031 · Cited by 4
Local measures of entanglement structure and dynamics in CFTs and black holesPreprint
Rolph, A. (2021) · arXiv (Cornell University) · Cited by 5
Geometric constraints via Page curves: insights from island rule and quantum focusing conjecture*
Yu, M., & Ge, X.-H. (2024) · Chinese Physics C · doi:10.1088/1674-1137/ada34e · Cited by 4
Replica wormhole as a vacuum-to-vacuum transition
An, Y., & Cheng, P. (2023) · The European Physical Journal C · doi:10.1140/epjc/s10052-023-11518-7 · Cited by 4
Mann, R. B. (2014) · Fundamental theories of physics · doi:10.1007/978-3-319-10852-0_3 · Cited by 3
Musings on Firewalls and the Information Paradox
Devin, M. (2014) · Galaxies · doi:10.3390/galaxies2020189 · Cited by 4
Hawking radiation and page curves of the black holes in thermal environment
Li, R., & Wang, J. (2021) · Communications in Theoretical Physics · doi:10.1088/1572-9494/abf823 · Cited by 4
Entropies and reflected entropies in the Hayden-Preskill protocol
Czech, B., Shuai, S., & Tang, H. (2024) · Journal of High Energy Physics · doi:10.1007/jhep02(2024)040 · Cited by 4
Small Schwarzschild de Sitter black holes, the future boundary and islands
Goswami, K., & Narayan, K. (2024) · Journal of High Energy Physics · doi:10.1007/jhep05(2024)016 · Cited by 4
Entanglement entropy in de Sitter: no pure states for conformal matter
Ageev, D. S., Aref’eva, I. Y., Belokon, A. I., Pushkarev, V. V., & Rusalev, T. A. (2024) · Journal of High Energy Physics · doi:10.1007/jhep05(2024)308 · Cited by 9
Unitarity and the information problem in an explicit model of black hole evaporation
Schindler, J., Frangipane, E., & Aguirre, A. (2021) · Classical and Quantum Gravity · doi:10.1088/1361-6382/abdf25 · Cited by 5
Is instability near a black hole key for ”thermalization” of its horizon?
Majhi, B. R. (2022) · General Relativity and Gravitation · doi:10.1007/s10714-022-02975-8 · Cited by 4
Single-Mode Squeezed Thermal States and Black Holes
Dhayal, R., Rathore, M., & Venkataratnam, K. K. (2019) · International Journal of Theoretical Physics · doi:10.1007/s10773-019-04303-4 · Cited by 4
A paradox regarding monogamy of entanglementPreprint
Karlsson, A. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1911.09226 · Cited by 4
Charged rotating quantum black holes
Bhattacharya, D., Hennigar, R. A., Mann, R. B., & Zhang, M. (2025) · Journal of High Energy Physics · doi:10.1007/jhep11(2025)165 · Cited by 5
Entanglement island and Page curve for one-sided charged black hole
Qu, Y.-F., Lan, Y.-L., Yu, H., Gan, W.-C., & Shu, F.-W. (2024) · Journal of High Energy Physics · doi:10.1007/jhep08(2024)023 · Cited by 3
Coarse-graining black holes out of equilibrium with boundary observables on time slice
Takeda, D. (2024) · Journal of High Energy Physics · doi:10.1007/jhep05(2024)319 · Cited by 3
Black holes and thermogeometric optimization
Avramov, V., Dimov, H., Radomirov, M., Rashkov, R. C., & Vetsov, T. (2025) · The European Physical Journal C · doi:10.1140/epjc/s10052-025-14303-w · Cited by 3
Zeno’s paradox and black hole information loss problem
Ge, X.-H. (2025) · Acta Physica Sinica · doi:10.7498/aps.74.20241751 · Cited by 4
Sharp Page transitions in generic Hamiltonian dynamics
Li, L. H., Kehrein, S. K., & Gopalakrishnan, S. (2025) · Physical review. B./Physical review. B · doi:10.1103/vnzh-y22h · Cited by 3
Effect of backreaction on island, Page curve and mutual information
Jain, P., Pant, S., & Parihar, H. (2025) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2025.116991 · Cited by 3
Capturing the Page curve and entanglement dynamics of black holes in quantum computers
Chowdhury, T. A., Yu, K., Asaduzzaman, M., & Sufian, R. S. (2025) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2025.117112 · Cited by 3
Density matrix of radiation of a black hole with a fluctuating horizon
Iofa, M. Z. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.94.064044 · Cited by 3
Upper bounds of holographic entanglement entropy growth rate for thermofield double states
Li, Z., & Yang, R.-Q. (2022) · Journal of High Energy Physics · doi:10.1007/jhep10(2022)072 · Cited by 3
Black hole production, eternal inflation, and information in quasi-de Sitter space
Seo, M. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/11/005 · Cited by 6
Matter–gravity entanglement entropy and the second law for black holes
Kay, B. S. (2023) · International Journal of Modern Physics D · doi:10.1142/s0218271823420026 · Cited by 3
Black holes, cavities, and blinking islands
Ageev, D. S., Aref’eva, I. Y., & Rusalev, T. A. (2025) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.111.026002 · Cited by 9
Page curves and replica wormholes from random dynamics
Jan De Boer, A., Hollander, J., & Rolph, A. (2024) · Journal of High Energy Physics · doi:10.1007/jhep07(2024)023 · Cited by 3
Island in warped AdS black holes
Anand, A. (2024) · International Journal of Modern Physics A · doi:10.1142/s0217751x24501331 · Cited by 3
Marto, J. (2021) · Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT) · Cited by 3
Puzzles and pitfalls involving Haar-typicality in holography
Bao, N., & Chatwin-Davies, A. (2018) · SciPost Physics · doi:10.21468/scipostphys.4.6.033 · Cited by 4
How not to extract information from black holes: Cosmic censorship as a guiding principle
Gennaro, S. D., & Ong, Y. C. (2022) · Physics Letters B · doi:10.1016/j.physletb.2022.137112 · Cited by 5
Quantum Black HolesPreprint
Ydri, B. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1708.00748 · Cited by 7
Future Boundaries and the Black Hole Information ParadoxPreprint
Perry, M. J. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2108.05744 · Cited by 16
Proceedings of the East Asia Joint Symposium on Fields and Strings 2021
Online, E. A. J. S. O. F. A. S. 2. O., Iso, S., Itoyama, H., Maruyoshi, K., Nishinaka, T., Oota, T., Sakai, K., Tsuchiya, A., & Yoshioka, R. (2022) · doi:10.1142/13004 · Cited by 3
Non-trivial saddles in microscopic description of black holes
Kumar, P., & Mondal, S. (2024) · Journal of High Energy Physics · doi:10.1007/jhep07(2024)123 · Cited by 2
Quantum focusing conjecture in two-dimensional evaporating black holes
Ishibashi, A., Matsuo, Y., & Tanaka, A. (2024) · Journal of High Energy Physics · doi:10.1007/jhep09(2024)126 · Cited by 2
Islands for black holes in a hybrid quantum state
Potaux, Y., Sarkar, D., & Solodukhin, S. N. (2025) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.111.026019 · Cited by 4
Liouville theory on a horizon: point particle/scalar field duality and Page-like curve
Roux, J.-B. (2024) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ad997a · Cited by 2
Finite entangling regions and information paradox in charged black holes
Belokon, A. I. (2025) · Theoretical and Mathematical Physics · doi:10.1134/s004057792501012x · Cited by 2
Probing the Page transition via approximate quantum error correction
Zhong, H. (2025) · Journal of High Energy Physics · doi:10.1007/jhep01(2025)086 · Cited by 2
Entanglement of defect subregions in double holography
Liu, Y., Chen, Q., Ling, Y., Peng, C., Tian, Y., & Xian, Z.-Y. (2024) · Journal of High Energy Physics · doi:10.1007/jhep07(2024)274 · Cited by 2
Time evolution of the Von Neumann entropy for a Kerr–Taub–NUT black hole
Arévalo, V. A., Andrade, D., & Rojas, C. (2024) · The European Physical Journal C · doi:10.1140/epjc/s10052-024-13290-8 · Cited by 4
Globally hyperbolic evaporating black hole and the information loss issue
Pêgas, J. V. O., Landulfo, A. G. S., Matsas, G. E. A., & Vanzella, D. A. T. (2025) · Classical and Quantum Gravity · doi:10.1088/1361-6382/adb534 · Cited by 2
Universal structure of islands in evaporating black holes
Matsuo, Y. (2025) · Journal of High Energy Physics · doi:10.1007/jhep03(2025)068 · Cited by 5
Tunneling of Bell particles, page curve and black hole information
Chu, C., & Miao, R.-X. (2025) · Physics Letters B · doi:10.1016/j.physletb.2025.139486 · Cited by 8
Evaporating black holes and late-stage loss of soft hair
Cheng, P. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.l061904 · Cited by 2
Missed opportunities of overcoming deadlocks
Aref’eva, I. Y. (2022) · International Journal of Modern Physics A · doi:10.1142/s0217751x22430047 · Cited by 2
The Nature and Origin of Time-Asymmetric Spacetime Structures
Zeh, H. D. (2014) · Springer handbooks · doi:10.1007/978-3-642-41992-8_10 · Cited by 2
Demonstration of the Hayden-Preskill Protocol via Mutual Information
Bae, J.-M., Kang, S., Yeom, D.-H., & Zoe, H. (2019) · Journal of the Korean Physical Society · doi:10.3938/jkps.75.941 · Cited by 2
Island formula from Wald-like entropy with backreaction
Hirano, S. (2024) · Journal of High Energy Physics · doi:10.1007/jhep02(2024)125 · Cited by 2
Quantum Black Holes as Solvents
Aurell, E., Eckstein, M., & Horodecki, P. (2021) · Foundations of Physics · doi:10.1007/s10701-021-00456-7 · Cited by 2
Black holes to white holes I. A complete quasi-classical modelPreprint
Bardeen, J. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2006.16804 · Cited by 4
Baby universes, ensemble averages and factorizations with mattersPreprint
Peng, C., Tian, J., & Yu, J. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2111.14856 · Cited by 15
Chen, P., Ong, Y. C., Page, D. N., Sasaki, M., & Yeom, D.-H. (2016) · International Journal of Modern Physics D · doi:10.1142/s0218271816450036 · Cited by 1
Self-citationHolography and the Page curve of an evaporating black hole
Khodahami, A. A., & Azizi, A. (2024) · International Journal of Modern Physics D · doi:10.1142/s0218271825500038 · Cited by 2
Saha, A., Chowdhury, A. R., & Gangopadhyay, S. (2025) · The European Physical Journal C · doi:10.1140/epjc/s10052-025-14579-y · Cited by 1
Quantum Kerr black hole from matrix theory of quantum gravity
Chu, C. (2025) · Physical review. D/Physical review. D. · doi:10.1103/5rwl-tr4y · Cited by 1
Modeling an internal structure of a black hole using a thermodynamic quasi-particle model
Bondarenko, S., Cheskis, D., & Singh, R. (2026) · Annals of Physics · doi:10.1016/j.aop.2026.170500 · Cited by 1
Page curve like dynamics in interacting quantum systems
Ray, T., Dhar, A., & Kulkarni, M. (2025) · Physical review. B./Physical review. B · doi:10.1103/z3sj-gn7t · Cited by 1
Page curves and island's delays in asymptotically flat 2d spacetimes with injections
Saito, Y. (2025) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptaf174 · Cited by 1
Quantum trajectories and Page-curve entanglement dynamics
Ganguly, K., Gopalakrishnan, P., Naik, A., Agarwalla, B. K., & Kulkarni, M. (2025) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/ae1ffa · Cited by 1
Entanglement, defects, and $$ T\overline{T} $$ on a black hole background
Dey, A. (2026) · Journal of High Energy Physics · doi:10.1007/jhep02(2026)242 · Cited by 1
Islands in Kerr–Newman black holes
Yu, M., & Ge, X.-H. (2026) · The European Physical Journal C · doi:10.1140/epjc/s10052-026-15432-6 · Cited by 1
A reverse black hole information problem
Jan De Boer, A., Hollander, J., & Rolph, A. (2026) · SciPost Physics · doi:10.21468/scipostphys.21.1.020 · Cited by 1
On the stability of (M theory) stars against collapse: Role of anisotropic pressures
Rama, S. K. (2015) · International Journal of Modern Physics A · doi:10.1142/s0217751x15501651 · Cited by 1
Disentanglement and Black Holes: Information Problem
Radosz, A., Gusin, P., & Roszak, K. (2017) · Acta Physica Polonica A · doi:10.12693/aphyspola.132.132 · Cited by 1
Final-State Condition and Dissipative Quantum Mechanics
Ho, P.-M. (2022) · Entropy · doi:10.3390/e24101411 · Cited by 1
The Nature and Origin of Time-Asymmetric Spacetime Structures
Zeh, H. D. (2014) · Springer eBooks · doi:10.1007/978-3-662-46035-1_10 · Cited by 1
Multipartite Correlations in Parikh–Wilczek Non-Thermal Spectrum
Ming, X. (2024) · Entropy · doi:10.3390/e26080680 · Cited by 1
Black hole information, replica wormholes and macroscopic entanglement
Xavier Calmet, A., & Hsu, S. D. H. (2024) · International Journal of Modern Physics A · doi:10.1142/s0217751x25300017 · Cited by 1
Bounded islands in a dS 2 multiverse model
Jiang, W.-H., & Yun-song Piao, A. (2025) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.111.023542 · Cited by 4
Hamiltonian formulation of general relativity
Kiefer, C. (2025) · Oxford University Press eBooks · doi:10.1093/oso/9780198842132.003.0004 · Cited by 1
Estimating time in quantum chaotic systems and black holes
Tang, H., Vardhan, S., & Wang, J. (2025) · SciPost Physics · doi:10.21468/scipostphys.19.4.095 · Cited by 1
Chaotic crystallography: how the physics of information reveals structural order in materials
Varn, D. P., & Crutchfield, J. P. (2014) · Current Opinion in Chemical Engineering · doi:10.1016/j.coche.2014.11.002 · Cited by 36
Hawking radiation as stimulated emission
Wen, W.-Y. (2020) · Physics Letters B · doi:10.1016/j.physletb.2020.135348 · Cited by 1
Schwarzschild black hole states and entropies on a nice slice
Rosabal, J. A. (2020) · The European Physical Journal C · doi:10.1140/epjc/s10052-020-08742-w · Cited by 2
Dynamic noncommutative BTZ black holes
Ankur, & Dey, S. (2021) · Physics Letters B · doi:10.1016/j.physletb.2021.136391 · Cited by 1
Does Considering Quantum Correlations Resolve the Information Paradox?Preprint
Roy, A., Rahat, M. H., Alvi, M. A., & Matin, M. A. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1312.2176 · Cited by 1
Gennaro, S. D., & Ong, Y. C. (2021) · arXiv (Cornell University) · Cited by 1
Flame And Smoke Retardants: Inorganic
Weil, E. D., & Shen, K. K. (2018) · Kirk-Othmer Encyclopedia of Chemical Technology · doi:10.1002/0471238961.0114200920152122.a01.pub2 · Cited by 1
Hawking radiation from an evaporating black hole via Bogoliubov transformations
Eyheralde, R. (2022) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ac93e2 · Cited by 2
Javadi, H., & Tehrani, M. V. (2015)
Ong, Y. C. (2015) · Springer theses · doi:10.1007/978-3-662-48270-4_1
Hawking radiation, the information paradox, and black hole thermodynamics
Ydri, B. (2017) · Institute of Physics eBooks · doi:10.1088/978-0-7503-1478-7ch6
Alsing, P. M., & Fanto, M. L. (2016) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.2224399 · Cited by 1
Metadata
- Authors
- Page, D. N.
- Affiliations
- University of Alberta (CA)
- Corresponding author
- Page, Don N
- ORCID
- Page, Don N
- Venue
- Journal of Cosmology and Astroparticle Physics
- Publisher
- IOP Publishing
- Published
- 2013-09-24
- Volume
- 2013
- Issue
- 09
- Pages
- 028-028
- ISSN
- 1475-7508 (ISSN-L)
- 1475-7516
- OpenAlex
- W2110969537
- Cited by
- 354
- References
- 243
- Citations by year
- 2026: 19 · 2025: 56 · 2024: 50 · 2023: 40 · 2022: 52 · 2021: 45 · 2020: 22 · 2019: 8 · 2018: 6 · 2017: 14 · 2016: 9 · 2015: 14 · 2014: 15 · 2013: 3
- FWCI
- 6.22
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Journal of Cosmology and Astroparticle Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Astrophysical Phenomena and Observations
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
- Keywords
- Hawking radiation, black hole evaporation, von Neumann entropy, Bekenstein-Hawking entropy, black hole information paradox, quantum scrambling, unitary evolution
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
