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REVIEW 2 major objections 4 minor 119 references

Black hole tunneling in loop quantum gravity

T0 review · 2 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Entropy of a quantum-corrected black hole gains a logarithmic term in a semiclassical tunneling calculation.

desk verdict The advertised √2πα log-correction in Eq. (3.24) is wrong by a factor 2√2 — the residue in Eq. (3.14) is mishandled — but the corrected coefficient restores consistency with the metric's surface gravity, so the paper is fixable. read the letter →

arxiv 2411.18116 v2 pith:HOYTGYTZ submitted 2024-11-27 gr-qc

Hongwei Tan , Rong-Zhen Guo , Jingyi Zhang This is my paper · ORCID
classification gr-qc
keywords blackholeentropyHawkingradiationquantumtunnelingemissionrateloopgravitylogarithmiccorrectionOppenheimer-Snyder
topics Quantum Gravity
open problems Quantum Gravity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper applies the semiclassical tunneling method of Parikh and Wilczek to the quantum Oppenheimer-Snyder black hole, a spherically symmetric collapse model whose exterior metric carries a loop-quantum-gravity correction proportional to αM²/r⁴. The authors compute the emission rate of massless scalar particles and find that, in addition to the classical Hawking spectrum, a quantum correction appears as a difference of logarithms of the Schwarzschild horizon area before and after emission. Interpreting the emission rate as exp(ΔS) in the usual statistical way, they extract the entropy of the black hole as S̃ = S + (√2πα/l_p²) log(A_Sch/l_p²) + O(α²), a logarithmic correction whose coefficient is fixed by the LQG parameter α. The significance is that this quantum-gravity-type entropy correction is obtained by a simple semiclassical calculation rather than by counting microstates, and it is consistent with several other approaches to quantum-corrected black hole entropy.

What carries the argument

The central mechanism is the Parikh–Wilczek tunneling computation: the emission rate is Γ ∼ exp(−2 Im A/ℏ), where Im A is the imaginary part of the particle action obtained by a contour integration around the pole in the null geodesic at the shifted horizon u = √(2(M−ω′)). The load-bearing identity is the statistical relation Γ ∼ exp(ΔS), which converts the emission rate into an entropy difference and yields the logarithmic correction of Eq. (3.24). The computation also relies on the Painlevé–Gullstrand coordinate transformation, which removes the coordinate singularity at the horizon so that the s-wave tunneling across the horizon can be treated in the WKB approximation.

What would settle it

Recompute Im A by evaluating the exact integrand of Eq. (3.10) without Taylor expanding in α, or by performing the contour integral numerically for a fixed small α; if the coefficient of the logarithmic term in the emission rate is πα/l_p² rather than √2πα/l_p² (as a direct comparison with the surface gravity would suggest), then Eq. (3.24) must be revised.

Watch

Extended reading notes

Core claim

Working with the quantum Oppenheimer-Snyder metric in Painlevé–Gullstrand coordinates, the paper calculates the imaginary part of the action for an outgoing massless s-wave particle that tunnels across the outer horizon, keeping the quantum-correction parameter α to first order. The resulting emission rate is Γ ∼ exp(−8πMω/l_p² (1 − ω/2M) + (√2πα/l_p²)[log(A_Sch(M−ω)/l_p²) − log(A_Sch(M)/l_p²)] + O(α²)). Using the Boltzmann-like relation Γ ∼ exp(ΔS) between the emission rate and the entropy change, the paper assigns the black hole an entropy S̃ = S + (√2πα/l_p²) log(A_Sch/l_p²) + O(α²), where S = 4πM²/l_p² is the classical Schwarzschild entropy. The coefficient √2πα/l_p² is positive, in contrast to the sign found in some loop-quantum-gravity microstate counts, and the paper argues on the basis of existing results that this sign may encode the combined contribution of quantum gravity effects and effective thermal fluctuations.

Load-bearing premise

The derivation stands on a single contour-integral step: when the α-order term in the tunneling action is integrated around the pole at the shifted horizon u = √(2(M−ω′)) with the Feynman iϵ prescription, the residue must produce the coefficient √2πα/(M−ω′); if that residue evaluation is wrong, the logarithmic coefficient and the entropy formula both change.

Editorial extensions

If this is right

  • If Eq. (3.24) is correct, the emission spectrum of the quantum OS black hole is not purely thermal: the logarithmic term modifies the rate in a way that depends on the area of the Schwarzschild horizon before and after emission.
  • The tunneling method, which is fully semiclassical, reproduces a quantum-gravity correction to entropy that other approaches obtain only by counting horizon microstates, so the method is validated as a probe of quantum gravity effects.
  • The logarithmic coefficient has a definite sign and magnitude set by the LQG parameter α, so a measurement or independent computation of this coefficient would test the value of the Barbero-Immirzi parameter, assuming the other steps in the derivation are sound.
  • Because the correction is positive, the entropy of the quantum OS black hole is larger than the classical value, which slows the decrease of entropy during evaporation and is consistent with a remnant scenario at late times if the M ≫ ω assumption is relaxed.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The authors do not perform a microstate count, so their positive log coefficient is a prediction that could be checked against a full loop-quantum-gravity computation of the horizon states for this specific metric; such a check would either support or rule out the interpretation that the coefficient combines quantum-gravity and thermal-fluctuation effects.
  • A natural extension is to repeat the calculation for massive particles or for particles tunneling across the inner horizon; if the inner horizon produces a different coefficient, the single-horizon entropy (3.24) would be only part of a more complete multi-horizon thermodynamics.
  • One could compute the same tunneling rate to next order in α; if the O(α²) term also contains a log A contribution, then the claim that the leading correction is purely logarithmic would need refinement.
  • The comparison with modified-dispersion-relation and GUP approaches suggests that the coefficient √2πα/l_p² can be used to fix the free parameter α₂ of the MDR or β of the GUP, providing a concrete bridge between this semiclassical result and other quantum-gravity phenomenology.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper applies the Parikh-Wilczek tunneling method to the quantum-corrected Oppenheimer-Snyder black hole metric (1.1), which contains an LQG correction term αM²/r⁴. The authors compute the emission rate of massless scalar particles, obtain a correction to the standard semiclassical rate, and then use the relation Γ ∼ e^{ΔS} to infer a logarithmic correction to the black hole entropy. The headline result, Eq. (3.24) and Eq. (1.3), is S̃ = S + (√2πα/l_p²) log(A_Sch/l_p²) + O(α²). The paper also compares this result with entropy corrections from noncommutative geometry, modified dispersion relations, GUP, and polymeric quantization.

Significance. If the computation were correct, the paper would provide a semiclassical derivation of a logarithmic entropy correction without microstate counting, and it would connect the Parikh-Wilczek approach to LQG-inspired black hole models. The manuscript is clearly organized, gives an explicit Painlevé-Gullstrand transformation, and is honest about its assumptions, notably the restriction to the outer horizon and the M² ≫ α regime. However, the central quantitative claim is not supported by the calculation as written: the α-order contour integral that fixes the prefactor of the logarithmic correction is evaluated incorrectly. The stated prefactor also conflicts with the surface gravity of the same metric. These issues affect the main result and the abstract, so the paper cannot be accepted in its present form.

major comments (2)
  1. [Sec. 3.2, Eqs. (3.13)-(3.14)] The α-order pole contribution is evaluated incorrectly. In Eq. (3.13), the α-dependent part of the second term is −α G(u)/(u−a)² with G(u) = (M−ω′)³ᐟ²/(√2 u⁴) and a = √(2(M−ω′+iε)). Under the same iε prescription that produces the leading term 4π(M−ω′), the second-order pole contributes Im ∫ G(u)/(u−a)² du = π G′(a) = −π/[2(M−ω′)], so the α coefficient in Eq. (3.14) should be +πα/[2(M−ω′)] rather than √2πα/(M−ω′). The factor of 2√2 is not a matter of convention. This error is quantitatively load-bearing: the low-energy limit of Eq. (3.16) gives an inverse-temperature shift δβ = 2√2πα/(M l_p²), whereas the surface gravity of Eq. (1.1) at r_h = 2M − α/(8M) + O(α²) gives κ = 1/(4M) − α/(32M³) + O(α²) and hence δβ = πα/(M l_p²). The advertised entropy prefactor in Eq. (3.24) and in the abstract is therefore not supported.
  2. [Sec. 3.3, Eqs. (3.17)-(3.25)] The entropy extraction rests on the ansatz Γ ∼ e^{ΔS}, specifically the phase-space factor e^{S_f}/e^{S_i} in Eqs. (3.18)-(3.19). This means the logarithmic correction is not an independent derivation from microstates; it is a repackaging of the semiclassical emission rate under a statistical interpretation. The paper should state this limitation explicitly and distinguish 'inferred from the tunneling rate under the phase-space ansatz' from 'derived from quantum gravity.' This is a methodological caveat, but it is central to the claim that the result supports the validity of the semiclassical method.
minor comments (4)
  1. [Title and Abstract] There are several typographical errors, including 'Oppenheimer-Snyde' in the title and abstract, 'emisson rate' in Sec. 3.2, and 'probality' in Sec. 3.3; these should be corrected.
  2. [Sec. 3.2, Eq. (3.16)] The units of ℏ and l_p² are used interchangeably; with G=c=1 and ℓ_p=√ℏ the two are identical, but this should be stated explicitly so that the factors in Eqs. (3.16) and (3.24) are unambiguous.
  3. [Sec. 3.4, comparison paragraphs] The comparisons with noncommutative, MDR, GUP, and polymeric entropy formulas are qualitative and do not map the parameters of those frameworks to α; the phrase 'consistent with our finding' should be softened unless a quantitative correspondence is provided.
  4. [Sec. 3.3, paragraph after Eq. (3.24)] The discussion of a positive versus negative logarithmic prefactor is somewhat speculative; the statement that the result 'might suggest' a decomposition a_q + a_f = √2πα/l_p² should be flagged as an interpretation, not a derivation.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the logarithmic entropy correction is read off from the independently computed tunneling rate, and the cited method [1,2] is re-derived inside the paper.

full rationale

The derivation chain is self-contained. The metric (1.1) is taken from the quantum OS model; the paper then computes the imaginary part of the action (3.10)-(3.15) and the emission rate (3.16) directly from the radial null geodesic (3.6). The entropy formula (3.24) is introduced after this calculation, with the coefficient sqrt(2*pi*alpha)/l_p^2 fixed by the alpha-dependent term in Im A, so it is an inference from the emission rate rather than an input fitted to the target result. The identity Gamma ~ exp(Delta S) is not merely imported from the self-citations [1,2]; it is re-derived in Eqs. (3.17)-(3.23), so the self-citation is not load-bearing. No free parameter is fitted to data, and the logarithmic correction is not defined in terms of the entropy formula it is supposed to establish. Any concern about the sign or magnitude of the alpha-term, such as whether the second-order pole in Eq. (3.13) should produce sqrt(2)*pi*alpha or pi*alpha/2, is a question of contour-integral correctness, not circularity; the claim would fail on mathematical accuracy, not by construction.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The central calculation rests on the LQG-corrected metric from prior work, the validity of the WKB tunneling method and Feynman prescription for this metric, and the identification of the emission rate with an entropy difference. No new entities are introduced, and no parameters are fitted to data in this paper; α is inherited from the model.

assumptions (4)
  • domain assumption The quantum OS metric (1.1) from Ref. [54] correctly describes the exterior spacetime of a collapsing dust ball with LQG corrections.
    The entire calculation inherits the LQC-deformed Friedmann equation and junction conditions from Lewandowski et al. The paper does not re-derive or test this metric.
  • domain assumption The generalized Birkhoff theorem of Ref. [95] ensures the exterior region is uniquely characterized by the mass M, so that the only back-reaction during tunneling is M → M-ω.
    Invoked in Sec. 3.2 to justify ignoring graviton emission and treating the process as a single-parameter mass change.
  • domain assumption The Parikh-Wilczek WKB tunneling method and the Feynman iϵ contour prescription remain valid for this modified metric.
    The emission rate is computed with WKB and contour deformation in Sec. 3.2; validity for the LQG-corrected metric is assumed rather than proven.
  • domain assumption The emission rate can be identified with exp(ΔS~) in order to define the entropy correction.
    The paper follows Refs [1,2] in using Γ ∼ e^{ΔS} to extract entropy from the rate, without independent thermodynamic derivation.

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Pith. "Pith review of Black hole tunneling in loop quantum gravity." pith.science (2026). https://pith.science/paper/HOYTGYTZ

@misc{pith2026241118116,
  author       = {Pith},
  title        = {Pith review of: Black hole tunneling in loop quantum gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HOYTGYTZ}},
  note         = {Machine review of arXiv:2411.18116}
}
read the original abstract

In this paper, we investigate the Hawking radiation of the quantum Oppenheimer- Snyde black hole with the tunneling scheme by Parikh and Wilczek. We calculate the emission rate of massless scalar particles. Compared to the traditional results within the framework of General Relativity, our findings include quantum correction terms arising from loop quantum gravity effects. Following the approach in [1, 2], we establish the entropy of the black hole. This entropy includes a logarithmic correction, which arises from quantum gravity effects. Our result is consistent with the well-known result in the context of quantum gravity.

Discussion (0). Continue with ORCID to comment.

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Works this paper leans on

119 extracted references · 65 canonical work pages

  1. [1]

    Zhang, Black hole quantum tunnelling and black hole entropy correction , Physics Letters B 668 (2008), no

    J. Zhang, Black hole quantum tunnelling and black hole entropy correction , Physics Letters B 668 (2008), no. 5 353–356

    2008

  2. [2]

    Zhang, Black hole entropy, log correction and inverse area correction , Physics Letters B 675 (2009), no

    J. Zhang, Black hole entropy, log correction and inverse area correction , Physics Letters B 675 (2009), no. 1 14–17

    2009

  3. [3]

    R. M. Wald, General relativity. University of Chicago press, 2010

    2010

  4. [4]

    Poisson, A relativist’s toolkit: the mathematics of black-hole mechanics

    E. Poisson, A relativist’s toolkit: the mathematics of black-hole mechanics . Cambridge university press, 2004

    2004

  5. [5]

    V. P. Frolov and A. Zelnikov, Introduction to black hole physics . OUP Oxford, 2011

    2011

  6. [6]

    Afshordi, A

    N. Afshordi, A. Ashtekar, E. Barausse, E. Berti, R. Brito, L. Buoninfante, R. Carballo-Rubio, V. Cardoso, G. Carullo, M. Dafermos, et al., Black holes inside and out 2024: visions for the future of black hole physics , arXiv preprint arXiv:2410.14414 (2024)

    arXiv 2024

  7. [7]

    Chandrasekhar and K

    S. Chandrasekhar and K. S. Thorne, The mathematical theory of black holes , 1985

    1985

  8. [8]

    LIGO Scientific, Virgo Collaboration, B. P. Abbott et al., Observation of Gravitational Waves from a Binary Black Hole Merger , Phys. Rev. Lett. 116 (2016), no. 6 061102, [ arXiv:1602.03837]

    arXiv 2016

Show all 119 references
  1. [9]

    LIGO Scientific, Virgo Collaboration, B. P. Abbott et al., GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence , Phys. Rev. Lett. 116 (2016), no. 24 241103, [ arXiv:1606.04855]

    2016 arXiv

  2. [10]

    LIGO Scientific, Virgo Collaboration, B. P. Abbott et al., Binary Black Hole Mergers in the first Advanced LIGO Observing Run , Phys. Rev. X 6 (2016), no. 4 041015, [ arXiv:1606.04856]. [Erratum: Phys.Rev.X 8, 039903 (2018)]

    2016 arXiv

  3. [11]

    LIGO Scientific, VIRGO Collaboration, B. P. Abbott et al., GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2 , Phys. Rev. Lett. 118 (2017), no. 22 221101, [arXiv:1706.01812]. [Erratum: Phys.Rev.Lett. 121, 129901 (2018)]

    2017 arXiv

  4. [12]

    B. P. Abbott, R. Abbott, T. Abbott, M. Abernathy, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, et al., Observation of gravitational waves from a binary black hole merger, Physical review letters 116 (2016), no. 6 061102

    2016

  5. [13]

    E. H. T. Collaboration et al., First m87 event horizon telescope results. i. the shadow of the supermassive black hole , arXiv preprint arXiv:1906.11238 (2019)

    2019 arXiv

  6. [14]

    Akiyama, A

    K. Akiyama, A. Alberdi, W. Alef, K. Asada, R. Azulay, A.-K. Baczko, D. Ball, M. Balokovi´ c, J. Barrett, D. Bintley, et al., First m87 event horizon telescope results. ii. array and instrumentation, The Astrophysical Journal Letters 875 (2019), no. 1 L2

    2019

  7. [15]

    Akiyama, A

    K. Akiyama, A. Alberdi, W. Alef, K. Asada, R. Azulay, A.-K. Baczko, D. Ball, M. Balokovi´ c, J. Barrett, D. Bintley, et al., First m87 event horizon telescope results. iii. data processing and calibration, The Astrophysical Journal Letters 875 (2019), no. 1 L3

    2019

  8. [16]

    Akiyama, A

    K. Akiyama, A. Alberdi, W. Alef, K. Asada, R. Azulay, A.-K. Baczko, D. Ball, M. Balokovi´ c, J. Barrett, D. Bintley, et al., First m87 event horizon telescope results. iv. imaging the central supermassive black hole , The Astrophysical Journal Letters 875 (2019), no. 1 L4

    2019

  9. [17]

    Akiyama, A

    K. Akiyama, A. Alberdi, W. Alef, K. Asada, R. Azulay, A.-K. Baczko, D. Ball, M. Balokovi´ c, J. Barrett, D. Bintley, et al., First m87 event horizon telescope results. v. physical origin of the asymmetric ring , The Astrophysical Journal Letters 875 (2019), no. 1 L5

    2019

  10. [18]

    Akiyama, A

    K. Akiyama, A. Alberdi, W. Alef, K. Asada, R. Azulay, A.-K. Baczko, D. Ball, M. Balokovi´ c, J. Barrett, D. Bintley, et al., First m87 event horizon telescope results. vi. the shadow and mass of the central black hole , The Astrophysical Journal Letters 875 (2019), no. 1 L6. – 12 –

    2019

  11. [19]

    Punturo et al., The Einstein Telescope: A third-generation gravitational wave observatory , Class

    M. Punturo et al., The Einstein Telescope: A third-generation gravitational wave observatory , Class. Quant. Grav. 27 (2010) 194002

    2010

  12. [20]

    Evans et al., Cosmic Explorer: A Submission to the NSF MPSAC ngGW Subcommittee , arXiv:2306.13745

    M. Evans et al., Cosmic Explorer: A Submission to the NSF MPSAC ngGW Subcommittee , arXiv:2306.13745

    arXiv

  13. [21]

    Evans et al., A Horizon Study for Cosmic Explorer: Science, Observatories, and Community , arXiv:2109.09882

    M. Evans et al., A Horizon Study for Cosmic Explorer: Science, Observatories, and Community , arXiv:2109.09882

    arXiv

  14. [22]

    Colpi et al., LISA Definition Study Report , arXiv:2402.07571

    M. Colpi et al., LISA Definition Study Report , arXiv:2402.07571

    arXiv

  15. [23]

    Luo et al., TianQin: a space-borne gravitational wave detector , Class

    TianQin Collaboration, J. Luo et al., TianQin: a space-borne gravitational wave detector , Class. Quant. Grav. 33 (2016), no. 3 035010, [ arXiv:1512.02076]

    2016 arXiv

  16. [24]

    Hu and Y.-L

    W.-R. Hu and Y.-L. Wu, The Taiji Program in Space for gravitational wave physics and the nature of gravity, Natl. Sci. Rev. 4 (2017), no. 5 685–686

    2017

  17. [25]

    Penrose, Gravitational collapse and space-time singularities , Physical Review Letters 14 (1965), no

    R. Penrose, Gravitational collapse and space-time singularities , Physical Review Letters 14 (1965), no. 3 57

    1965

  18. [26]

    S. W. Hawking and R. Penrose, The singularities of gravitational collapse and cosmology , Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 314 (1970), no. 1519 529–548

    1970

  19. [27]

    P. R. Brady and J. D. Smith, Black hole singularities: a numerical approach , Physical review letters 75 (1995), no. 7 1256

    1995

  20. [28]

    S. W. Hawking, Black hole explosions? , Nature 248 (1974), no. 5443 30–31

    1974

  21. [29]

    Hawking, Black holes and the information paradox , in General Relativity and Gravitation , pp

    S. Hawking, Black holes and the information paradox , in General Relativity and Gravitation , pp. 56–62. World Scientific, 2005

    2005

  22. [30]

    J. D. Bekenstein, Black holes and information theory , Contemporary Physics 45 (2004), no. 1 31–43

    2004

  23. [31]

    Landgren, The information paradox, a modern review ,

    F. Landgren, The information paradox, a modern review ,

  24. [32]

    Thiemann, Modern canonical quantum general relativity

    T. Thiemann, Modern canonical quantum general relativity . Cambridge University Press, 2008

    2008

  25. [33]

    Rovelli, Quantum gravity

    C. Rovelli, Quantum gravity. Cambridge university press, 2004

    2004

  26. [34]

    M. Han, Y. Ma, and W. Huang, Fundamental structure of loop quantum gravity , International Journal of Modern Physics D 16 (2007), no. 09 1397–1474

    2007

  27. [35]

    Thiemann, Lectures on loop quantum gravity , in Quantum gravity: From theory to experimental search, pp

    T. Thiemann, Lectures on loop quantum gravity , in Quantum gravity: From theory to experimental search, pp. 41–135. Springer, 2003

    2003

  28. [36]

    Ashtekar and J

    A. Ashtekar and J. Lewandowski, Background independent quantum gravity: a status report , Classical and Quantum Gravity 21 (2004), no. 15 R53

    2004

  29. [37]

    Giesel and H

    K. Giesel and H. Sahlmann, From classical to quantum gravity: introduction to loop quantum gravity, arXiv preprint arXiv:1203.2733 (2012)

    2012 arXiv

  30. [38]

    Rovelli, Zakopane lectures on loop gravity , arXiv preprint arXiv:1102.3660 (2011)

    C. Rovelli, Zakopane lectures on loop gravity , arXiv preprint arXiv:1102.3660 (2011)

    2011 arXiv

  31. [39]

    Perez, The spin-foam approach to quantum gravity , Living Reviews in Relativity 16 (2013) 1–128

    A. Perez, The spin-foam approach to quantum gravity , Living Reviews in Relativity 16 (2013) 1–128

    2013

  32. [40]

    Husain, J

    V. Husain, J. G. Kelly, R. Santacruz, and E. Wilson-Ewing, Quantum gravity of dust collapse: shock waves from black holes , Physical Review Letters 128 (2022), no. 12 121301

    2022

  33. [41]

    Husain, J

    V. Husain, J. G. Kelly, R. Santacruz, and E. Wilson-Ewing, Fate of quantum black holes , Physical Review D 106 (2022), no. 2 024014

    2022

  34. [42]

    Rovelli, Black hole entropy from loop quantum gravity , Physical Review Letters 77 (1996), no

    C. Rovelli, Black hole entropy from loop quantum gravity , Physical Review Letters 77 (1996), no. 16 3288

    1996

  35. [43]

    Perez, Black holes in loop quantum gravity , Reports on Progress in Physics 80 (2017), no

    A. Perez, Black holes in loop quantum gravity , Reports on Progress in Physics 80 (2017), no. 12 126901. – 13 –

    2017

  36. [44]

    Rovelli and F

    C. Rovelli and F. Vidotto, Planck stars , International Journal of Modern Physics D 23 (2014), no. 12 1442026

    2014

  37. [45]

    H. M. Haggard and C. Rovelli, Quantum-gravity effects outside the horizon spark black to white hole tunneling, Physical Review D 92 (2015), no. 10 104020

    2015

  38. [46]

    De Lorenzo and A

    T. De Lorenzo and A. Perez, Improved black hole fireworks: Asymmetric black-hole-to-white-hole tunneling scenario, Physical Review D 93 (2016), no. 12 124018

    2016

  39. [47]

    Christodoulou, C

    M. Christodoulou, C. Rovelli, S. Speziale, and I. Vilensky, Planck star tunneling time: An astrophysically relevant observable from background-free quantum gravity , Physical Review D 94 (2016), no. 8 084035

    2016

  40. [48]

    Bianchi, M

    E. Bianchi, M. Christodoulou, F. d’Ambrosio, H. M. Haggard, and C. Rovelli, White holes as remnants: a surprising scenario for the end of a black hole , Classical and Quantum Gravity 35 (2018), no. 22 225003

    2018

  41. [49]

    D’Ambrosio, M

    F. D’Ambrosio, M. Christodoulou, P. Martin-Dussaud, C. Rovelli, and F. Soltani, End of a black hole’s evaporation, Phys. Rev. D 103 (May, 2021) 106014

    2021

  42. [50]

    Soltani, C

    F. Soltani, C. Rovelli, and P. Martin-Dussaud, End of a black hole’s evaporation. ii. , Physical Review D 104 (2021), no. 6 066015

    2021

  43. [51]

    Rignon-Bret and C

    A. Rignon-Bret and C. Rovelli, Black to white transition of a charged black hole , Physical Review D 105 (2022), no. 8 086003

    2022

  44. [52]

    M. Han, C. Rovelli, and F. Soltani, Geometry of the black-to-white hole transition within a single asymptotic region, Physical Review D 107 (2023), no. 6 064011

    2023

  45. [53]

    J. R. Oppenheimer and H. Snyder, On continued gravitational contraction, Physical Review 56 (1939), no. 5 455

    1939

  46. [54]

    Lewandowski, Y

    J. Lewandowski, Y. Ma, J. Yang, and C. Zhang, Quantum oppenheimer-snyder and swiss cheese models, Physical Review Letters 130 (2023), no. 10 101501

    2023

  47. [55]

    J. Yang, C. Zhang, and Y. Ma, Shadow and stability of quantum-corrected black holes , The European Physical Journal C 83 (2023), no. 7 619

    2023

  48. [56]

    Stashko, Quasinormal modes and gray-body factors of regular black holes in asymptotically safe gravity, Physical Review D 110 (2024), no

    O. Stashko, Quasinormal modes and gray-body factors of regular black holes in asymptotically safe gravity, Physical Review D 110 (2024), no. 8 084016

    2024

  49. [57]

    Zhang, Y

    C. Zhang, Y. Ma, and J. Yang, Black hole image encoding quantum gravity information , Physical Review D 108 (2023), no. 10 104004

    2023

  50. [58]

    H. Gong, S. Li, D. Zhang, G. Fu, and J.-P. Wu, Quasinormal modes of quantum-corrected black holes, Physical Review D 110 (2024), no. 4 044040

    2024

  51. [59]

    Yang, Y.-P

    S. Yang, Y.-P. Zhang, T. Zhu, L. Zhao, and Y.-X. Liu, Gravitational waveforms from periodic orbits around a quantum-corrected black hole , arXiv preprint arXiv:2407.00283 (2024)

    2024 arXiv

  52. [60]

    Liu, M.-Y

    H. Liu, M.-Y. Lai, X.-Y. Pan, H. Huang, and D.-C. Zou, Gravitational lensing effect of black holes in effective quantum gravity , Physical Review D 110 (2024), no. 10 104039

    2024

  53. [61]

    Zi and S

    T. Zi and S. Kumar, Eccentric extreme mass-ratio inspirals: A gateway to probe quantum gravity effects, arXiv preprint arXiv:2409.17765 (2024)

    2024 arXiv

  54. [62]

    Kantowski and R

    R. Kantowski and R. K. Sachs, Some spatially homogeneous anisotropic relativistic cosmological models, Journal of Mathematical Physics 7 (1966), no. 3 443–446

    1966

  55. [63]

    Joe, Anisotropic Spacetimes and Black Hole Interiors in Loop Quantum Gravity

    A. Joe, Anisotropic Spacetimes and Black Hole Interiors in Loop Quantum Gravity . PhD thesis, Louisiana State U., 2015

    2015

  56. [64]

    Modesto, The kantowski-sachs space-time in loop quantum gravity , International Journal of Theoretical Physics 45 (2006), no

    L. Modesto, The kantowski-sachs space-time in loop quantum gravity , International Journal of Theoretical Physics 45 (2006), no. 12 2235–2246. – 14 –

    2006

  57. [65]

    Casadio, A

    R. Casadio, A. Kamenshchik, and J. Ovalle, Cosmology from schwarzschild black hole revisited , Physical Review D 110 (2024), no. 4 044001

    2024

  58. [66]

    S. W. Hawking, Particle creation by black holes , Communications in mathematical physics 43 (1975), no. 3 199–220

    1975

  59. [67]

    G. W. Gibbons and S. W. Hawking, Action integrals and partition functions in quantum gravity , Physical Review D 15 (1977), no. 10 2752

    1977

  60. [68]

    M. K. Parikh and F. Wilczek, Hawking radiation as tunneling , Physical review letters 85 (2000), no. 24 5042

    2000

  61. [69]

    Parikh, A secret tunnel through the horizon , International Journal of Modern Physics D 13 (2004), no

    M. Parikh, A secret tunnel through the horizon , International Journal of Modern Physics D 13 (2004), no. 10 2351–2354

    2004

  62. [70]

    M. A. Rahman and M. I. Hossain, Hawking radiation of schwarzschild–de sitter black hole by hamilton–jacobi method, Physics Letters B 712 (2012), no. 1-2 1–5

    2012

  63. [71]

    S. P. Kim, Schwinger effect, hawking radiation and unruh effect , International Journal of Modern Physics D 25 (2016), no. 13 1645005

    2016

  64. [72]

    Hooft, On the quantum structure of a black hole , Nuclear Physics B 256 (1985) 727–745

    G. Hooft, On the quantum structure of a black hole , Nuclear Physics B 256 (1985) 727–745

    1985

  65. [73]

    Emparan, Black hole entropy as entanglement entropy: a holographic derivation , Journal of High Energy Physics 2006 (2006), no

    R. Emparan, Black hole entropy as entanglement entropy: a holographic derivation , Journal of High Energy Physics 2006 (2006), no. 06 012

    2006

  66. [74]

    Almheiri, T

    A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, The entropy of hawking radiation, Reviews of Modern Physics 93 (2021), no. 3 035002

    2021

  67. [75]

    Zhang and Z

    J.-Y. Zhang and Z. Zhao, Hawking radiation via tunneling from Kerr black holes , Mod. Phys. Lett. A 20 (2005) 1673–1681

    2005

  68. [76]

    Zhang and Z

    J.-Y. Zhang and Z. Zhao, Massive particles-prime black hole tunneling and de Sitter tunneling , Nucl. Phys. B 725 (2005) 173–180

    2005

  69. [77]

    Ghosh and P

    A. Ghosh and P. Mitra, Log correction to the black hole area law , Physical Review D—Particles, Fields, Gravitation, and Cosmology 71 (2005), no. 2 027502

    2005

  70. [78]

    R. K. Kaul and P. Majumdar, Logarithmic correction to the bekenstein-hawking entropy , Physical Review Letters 84 (2000), no. 23 5255

    2000

  71. [79]

    Domagala and J

    M. Domagala and J. Lewandowski, Black-hole entropy from quantum geometry , Classical and Quantum Gravity 21 (2004), no. 22 5233

    2004

  72. [80]

    K. A. Meissner, Black-hole entropy in loop quantum gravity , Classical and Quantum Gravity 21 (2004), no. 22 5245

    2004

  73. [81]

    Chatterjee and P

    A. Chatterjee and P. Majumdar, Universal canonical black hole entropy , Physical Review Letters 92 (2004), no. 14 141301

    2004

  74. [82]

    Medved, A comment on black hole entropy or does nature abhor a logarithm? , Classical and Quantum Gravity 22 (2004), no

    A. Medved, A comment on black hole entropy or does nature abhor a logarithm? , Classical and Quantum Gravity 22 (2004), no. 1 133

    2004

  75. [83]

    Lin and X

    J. Lin and X. Zhang, Effective four-dimensional loop quantum black hole with a cosmological constant, Physical Review D 110 (2024), no. 2 026002

    2024

  76. [84]

    Z. Shi, X. Zhang, and Y. Ma, Higher-dimensional quantum oppenheimer-snyder model , Physical Review D 110 (2024), no. 10 104074

    2024

  77. [85]

    Banerjee and B

    R. Banerjee and B. R. Majhi, Quantum tunneling and back reaction , Physics Letters B 662 (2008), no. 1 62–65

    2008

  78. [86]

    Banerjee and B

    R. Banerjee and B. R. Majhi, Quantum tunneling beyond semiclassical approximation , Journal of High Energy Physics 2008 (2008), no. 06 095. – 15 –

    2008

  79. [87]

    Banerjee and B

    R. Banerjee and B. R. Majhi, Quantum tunneling and trace anomaly , Physics Letters B 674 (2009), no. 3 218–222

    2009

  80. [88]

    B. R. Majhi, Fermion tunneling beyond semiclassical approximation , Physical Review D—Particles, Fields, Gravitation, and Cosmology 79 (2009), no. 4 044005

    2009

  81. [89]

    B. R. Majhi and S. Samanta, Hawking radiation due to photon and gravitino tunneling , Annals of Physics 325 (2010), no. 11 2410–2424

    2010

  82. [90]

    Ashtekar, T

    A. Ashtekar, T. Pawlowski, and P. Singh, Quantum nature of the big bang , Physical review letters 96 (2006), no. 14 141301

    2006

  83. [91]

    J. Yang, Y. Ding, and Y. Ma, Alternative quantization of the hamiltonian in loop quantum cosmology, Physics Letters B 682 (2009), no. 1 1–7

    2009

  84. [92]

    Assanioussi, A

    M. Assanioussi, A. Dapor, and K. Liegener, T. paw lowski, emergent de sitter epoch of the quantum cosmos, Phys. Rev. Lett 121 (2018) 081303

    2018

  85. [93]

    Israel, Singular hypersurfaces and thin shells in general relativity , Il Nuovo Cimento B (1965-1970) 44 (1966), no

    W. Israel, Singular hypersurfaces and thin shells in general relativity , Il Nuovo Cimento B (1965-1970) 44 (1966), no. 1 1–14

    1966

  86. [94]

    Painlev´ e,La m´ ecanique classique et la th´ eorie de la relativit´ e, Comptes Rendus Academie des Sciences (serie non specifiee) 173 (1921) 677–680

    P. Painlev´ e,La m´ ecanique classique et la th´ eorie de la relativit´ e, Comptes Rendus Academie des Sciences (serie non specifiee) 173 (1921) 677–680

    1921

  87. [95]

    Cafaro and J

    L. Cafaro and J. Lewandowski, Status of birkhoff ’s theorem in the polymerized semiclassical regime of loop quantum gravity , Physical Review D 110 (2024), no. 2 024072

    2024

  88. [96]

    Singha, Thermodynamics of multi-horizon spacetimes , General Relativity and Gravitation 54 (2022), no

    C. Singha, Thermodynamics of multi-horizon spacetimes , General Relativity and Gravitation 54 (2022), no. 4 38

    2022

  89. [97]

    Saghafi and K

    S. Saghafi and K. Nozari, Hawking-like radiation as tunneling from a cosmological black hole in modified gravity: semiclassical approximation and beyond , General Relativity and Gravitation 55 (2023), no. 1 20

    2023

  90. [98]

    Nozari and A

    K. Nozari and A. Sefidgar, On the existence of the logarithmic correction term in black hole entropy-area relation, General Relativity and Gravitation 39 (2007) 501–509

    2007

  91. [99]

    H. S. Snyder, Quantized space-time, Physical Review 71 (1947), no. 1 38

    1947

  92. [100]

    Seiberg and E

    N. Seiberg and E. Witten, String theory and noncommutative geometry , Journal of High Energy Physics 1999 (1999), no. 09 032

    1999

  93. [101]

    M. R. Douglas and N. A. Nekrasov, Noncommutative field theory , Reviews of Modern Physics 73 (2001), no. 4 977

    2001

  94. [102]

    Aschieri, C

    P. Aschieri, C. Blohmann, M. Dimitrijevi´ c, F. Meyer, P. Schupp, and J. Wess, A gravity theory on noncommutative spaces, Classical and Quantum Gravity 22 (2005), no. 17 3511

    2005

  95. [103]

    Nozari and S

    K. Nozari and S. H. Mehdipour, Hawking radiation as quantum tunneling from a noncommutative schwarzschild black hole , Classical and Quantum Gravity 25 (2008), no. 17 175015

    2008

  96. [104]

    Amelino-Camelia, M

    G. Amelino-Camelia, M. Arzano, Y. Ling, and G. Mandanici, Black-hole thermodynamics with modified dispersion relations and generalized uncertainty principles , Classical and Quantum Gravity 23 (2006), no. 7 2585

    2006

  97. [105]

    Nozari and A

    K. Nozari and A. Sefidgar, Comparison of approaches to quantum correction of black hole thermodynamics, Physics Letters B 635 (2006), no. 2-3 156–160

    2006

  98. [106]

    Nozari and S

    K. Nozari and S. Saghafi, Natural cutoffs and quantum tunneling from black hole horizon , Journal of High Energy Physics 2012 (2012), no. 11 1–18

    2012

  99. [107]

    Ashtekar, S

    A. Ashtekar, S. Fairhurst, and J. L. Willis, Quantum gravity, shadow states and quantum mechanics, Classical and Quantum Gravity 20 (2003), no. 6 1031

    2003

  100. [108]

    Corichi, T

    A. Corichi, T. Vukaˇ sinac, and J. A. Zapata,Polymer quantum mechanics and its continuum limit , Physical Review D—Particles, Fields, Gravitation, and Cosmology 76 (2007), no. 4 044016. – 16 –

    2007

  101. [109]

    Gorji, K

    M. Gorji, K. Nozari, and B. Vakili, Polymeric quantization and black hole thermodynamics , Physics Letters B 735 (2014) 62–68

    2014

  102. [110]

    Penington, Entanglement wedge reconstruction and the information paradox , Journal of High Energy Physics 2020 (2020), no

    G. Penington, Entanglement wedge reconstruction and the information paradox , Journal of High Energy Physics 2020 (2020), no. 9 1–84

    2020

  103. [111]

    Almheiri, N

    A. Almheiri, N. Engelhardt, D. Marolf, and H. Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole , Journal of High Energy Physics 2019 (2019), no. 12 1–47

    2019

  104. [112]

    Almheiri, R

    A. Almheiri, R. Mahajan, J. Maldacena, and Y. Zhao, The page curve of hawking radiation from semiclassical geometry, Journal of High Energy Physics 2020 (2020), no. 3 1–24

    2020

  105. [113]

    Almheiri, R

    A. Almheiri, R. Mahajan, and J. Maldacena, Islands outside the horizon , arXiv preprint arXiv:1910.11077 (2019)

    2019 arXiv

  106. [114]

    Hashimoto, N

    K. Hashimoto, N. Iizuka, and Y. Matsuo, Islands in schwarzschild black holes , Journal of High Energy Physics 2020 (2020), no. 6 1–21

    2020

  107. [115]

    Ryu and T

    S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy , Journal of High Energy Physics 2006 (2006), no. 08 045

    2006

  108. [116]

    V. E. Hubeny, M. Rangamani, and T. Takayanagi, A covariant holographic entanglement entropy proposal, Journal of High Energy Physics 2007 (2007), no. 07 062

    2007

  109. [117]

    Engelhardt and A

    N. Engelhardt and A. C. Wall, Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime , Journal of High Energy Physics 2015 (2015), no. 1 1–27

    2015

  110. [118]

    D. N. Page, Information in black hole radiation , Physical review letters 71 (1993), no. 23 3743

    1993

  111. [119]

    D. N. Page, Time dependence of hawking radiation entropy , Journal of Cosmology and Astroparticle Physics 2013 (2013), no. 09 028. – 17 –

    2013

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