Pith. sign in

REVIEW 4 major objections 4 minor 40 references

In AdS black holes with nonlinear electrodynamics, isentropic absorption of a charged particle is classically forbidden but proceeds by quantum tunneling; smaller holes tunnel more readily, and stronger nonlinearity suppresses it.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-03 09:25 UTC pith:3D6P7J7R

load-bearing objection Clean classical argument and a reasonable framework transfer, but the tunneling probabilities rest on an underived action formula, missing numerical parameters, and a direct EH contradiction. the 4 major comments →

arxiv 2601.13786 v2 pith:3D6P7J7R submitted 2026-01-20 hep-th

Nonperturbative Isentropic Processes in AdS Black Holes with Nonlinear Electrodynamics

Mozib Bin Awal , Prabwal Phukon This is my paper
classification hep-th PACS 04.70.Dy
keywords isentropic processesnonlinear electrodynamicsAdS black holesquantum tunnelingEuclidean actionentropy boundsblack hole information paradoxeffective potential
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The central claim is that isentropic absorption of a charged particle — the process that could push black hole entropy past the Bekenstein–Hawking bound — is classically impossible in four families of AdS black holes with nonlinear electrodynamics, but can occur through quantum tunneling. The tunneling probability is controlled by a Euclidean action integral over the classically forbidden region just outside the horizon. The paper finds numerically that stronger nonlinear-electrodynamics couplings suppress the tunneling probability (with only weak dependence in the Born–Infeld case and one inversion for Euler–Heisenberg), while increasing black hole charge mostly enhances it and increasing horizon radius strongly suppresses it. That last trend means smaller black holes behave less classically and are more likely to violate entropy bounds. The authors conjecture the behavior is universal across black hole spacetimes and relevant to the information loss paradox.

Core claim

In each of the four models — NED-AdS, ModMax-AdS, Euler-Heisenberg-AdS, and Born-Infeld-AdS — the paper considers a charged test particle with energy fixed by the isentropic condition E = qΦ(r+). Near the horizon the radial effective potential satisfies V_eff(r+)=0 and dV_eff/dr|_{r+}=4πT > 0, so V_eff is positive just outside the horizon: the particle is reflected at an outer turning point r2 and can never classically reach the hole. The quantum amplitude to tunnel through the barrier is evaluated in the semiclassical approximation, giving Γ ~ e^{-2S_E} with S_E = ∫_{r+}^{r2} dr/√V_eff. Numerically integrating this action for the four backgrounds, the paper reports that S_E increases as the

What carries the argument

The central object is the Euclidean action S_E = ∫_{r+}^{r2} dr/√V_eff, built from the radial effective potential V_eff(r) of a charged test particle under the isentropic energy condition E = qΦ. Its defining property is the near-horizon behaviour V_eff'(r+)=4πT > 0, which creates the classically forbidden interval [r2, r+]. This action enters the WKB transition amplitude as K ~ e^{-S_E}, giving a tunneling probability Γ ~ e^{-2S_E}; all reported parameter dependences are read off from numerical evaluation of this single integral.

Load-bearing premise

The load-bearing premise is the Euclidean-action prescription S_E = ∫_{r2}^{r+} dr/√V_eff stated in Eqs. (24)–(27) of Sec. III.1: the paper never derives this from the charged particle action in the curved background, never checks it against the known Reissner–Nordström limit, and leaves the numerical setup (AdS scale l, Newton constant G) unspecified, so the reported parameter dependences stand or fall with this formula.

What would settle it

Evaluate the barrier integral S_E = ∫_{r+}^{r2} dr/√V_eff for the Reissner–Nordström limit (all nonlinear couplings set to zero) and compare against the known RN result from Ref. [30]; if the numbers disagree, the Euclidean-action formula underlying all the plots is invalid. Alternatively, derive the Euclidean Lagrangian from the charged-particle worldline action in one of the NED backgrounds and check whether it reduces to Eq. (27).

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • In all four NLED-AdS backgrounds the isentropic absorption of a charged particle is classically forbidden; only tunneling permits it.
  • Stronger nonlinear electrodynamics generally lowers the tunneling probability, so the NLED couplings act as an entropy-bound enforcing mechanism.
  • Smaller black holes have larger tunneling rates, so the late stages of black hole evaporation are the regime where nonperturbative isentropic absorption is most relevant.
  • The Born–Infeld case shows that not every nonlinear electrodynamics modifies the barrier equally; the tunneling probability is nearly insensitive to β.
  • The results extend the earlier Reissner–Nordström and Kerr–Newman findings to NLED-modified spacetimes, supporting a universality conjecture.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • A direct extension would be to compare Γ_tunnel with the Hawking emission rate as a function of horizon radius; if the tunneling channel ever dominates for near-extremal black holes, it would give an observational handle on entropy-bound violations.
  • The Euler–Heisenberg inversion (larger a lowers S_E for fixed Q) is a natural stress test: a higher-resolution scan of the a–Q plane would show whether the universality conjecture survives or needs a caveat.
  • Because the numerical setup omits the AdS scale l and Newton constant G, the absolute values of S_E are not fixed; rescaling the action by the black hole temperature T would sharpen the parameter trends.
  • The small-black-hole trend suggests that remnant or final-stage black holes could absorb charge isentropically with appreciable probability; whether this alters information-paradox resolutions via remnants is a question the paper raises but leaves open.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. This paper studies isentropic absorption (dM = Φ dQ) of a charged test particle by four AdS black hole spacetimes with nonlinear electrodynamics: NED-AdS, ModMax-AdS, Euler-Heisenberg-AdS, and Born-Infeld-AdS. For each model the authors write down the radial effective potential of Eq. (10), observe that Veff(r+) = 0 and Veff'(r+) = 4πT > 0, and conclude that the process is classically forbidden, with a classically forbidden region between an outer turning point r2 and the horizon r+. They then assert a Euclidean-action formula S_E = ∫ dr/√Veff, evaluate it numerically, and interpret Γ ∼ e^{-2S_E}. The main claims are that stronger nonlinear-electrodynamics parameters suppress the tunnelling probability, that larger black hole charge enhances it, that smaller horizon radius enhances it, and that this small-black-hole behaviour may be universal and relevant to entropy bounds.

Significance. If established, the quantitative results would extend the nonperturbative entropy-bound-violation channel of Mann and Yeom to a broad class of NLED-AdS black holes and would identify a striking small-black-hole enhancement. The classical no-go part is sound: the near-horizon argument Veff(r+) = 0 and Veff'(r+) = 4πT > 0 is clean, although the general statement already appears in Ref. [31] for all stationary, nonextremal, axisymmetric black holes, so the novelty resides in the Euclidean-action computation. That computation, however, is the weakest point: the central formula is asserted rather than derived, the numerical setup is under-specified, and the paper contains a direct contradiction between the Euler-Heisenberg section and the conclusions. The claimed universality and entropy-bound implications are therefore not supported by the manuscript as it stands.

major comments (4)
  1. [Sec. III.1, Eqs. (19)-(27)] The quantitative core of the paper, S_E = ∫_{r2}^{r+} dr/√Veff, is never derived. The path-integral discussion in Eqs. (19)-(21) is schematic, and Eq. (27) is simply asserted; no Euclidean Lagrangian L_E, integration measure, affine parameter, or relation between L_E and Veff is provided. For a relativistic charged particle in a static metric, the standard WKB/instanton action is based on the canonical radial momentum, whose integrand has a different form (typically √Veff/f) and different parameter dependence. The formula is also not checked against the known Reissner-Nordström limit when b→0, η→0, a→0, or β→∞. Since every reported parameter dependence of the tunnelling probability is read off S_E, this unsupported prescription is load-bearing.
  2. [Secs. III.1-III.4 and Figs. 2-8] The numerical computations are not reproducible. The metric functions contain the AdS length l and Newton constant G (Eqs. (16), (31), (36), (41)), and M is determined by f(r+)=0, yet the manuscript never specifies l, G, or M for any of the plotted curves. Only m=0.0002 and q=0.005 are given, and the Born-Infeld figure captions do not even list those. Without these values the outer turning point r2, the Euclidean action, and the claimed monotonicities cannot be verified. In addition, no condition ensuring the existence of both turning points or of a non-extremal horizon is stated for the ranges of r+ and Q shown.
  3. [Sec. III.3 vs. Sec. IV] There is a direct internal contradiction for the Euler-Heisenberg model. In Sec. III.3 the text states that for fixed charge Q the Euclidean action decreases with increasing a, implying that increasing nonlinearity enhances tunnelling, and Fig. 6(a) is consistent with this. The concluding section, however, states that for the NED, ModMax, and Euler-Heisenberg systems the Euclidean action increases with the nonlinear parameters, leading to suppression. The abstract's blanket claim that tunnelling is 'increasingly suppressed as the strength of the non-linearity is enhanced' is therefore contradicted by the Euler-Heisenberg results as presented. This affects the claimed universality of the main result.
  4. [Sec. III.4, Eq. (42)] The Born-Infeld effective potential is written with a plus sign in front of the squared term, while Eq. (10) requires a minus sign: Veff = -(1/m^2)(E - qΦ)^2 + f(r). If the displayed expression was used in the numerics, the barrier shape and hence the Euclidean action for the Born-Infeld model would be affected. At minimum, the equation as printed is not the effective potential derived from Eq. (10).
minor comments (4)
  1. [Eq. (30)] The line element contains 'r^2(dθ^2 + r^2 sin^2 θ dφ^2)'; the extra r^2 inside the parentheses is a typographical error.
  2. [Sec. III.4] The text says 'we compute the Euclidean action in equation 37' but the intended reference is Eq. (27).
  3. [Figs. 2-8] Units and dimensions are not stated. Quantities such as Q, b, η, a, β, m, q, and r+ are treated as dimensionless in the plots, but the metric functions imply definite length/charge scales. The authors should specify the conventions or introduce dimensionless variables.
  4. [IV] The conclusion summarizes the Euler-Heisenberg charge dependence as 'the action increases beyond a certain Q', but the body text says the increase occurs after a non-monotonic regime; this should be reconciled for clarity.

Circularity Check

0 steps flagged

No circularity found: the derivation is self-contained and parameter scans are not fitted to the output.

full rationale

The paper's derivation chain is: (i) choose a known NLED-AdS metric and electrostatic potential; (ii) impose the isentropic condition E - qΦ = 0, yielding a positive effective potential barrier; (iii) compute the Euclidean action S_E = ∫_{r2}^{r+} dr / √V_eff following the external WKB prescription of Ref. [30]; (iv) numerically integrate and plot S_E versus b, η, a, β, Q, and r_+. None of the parameters are fitted to the plotted outcome; they are scanned inputs, and S_E is not re-injected as an input. Eq. (27) is imported from an external reference (Mann and Yeom), not from the present authors' prior work, so there is no self-citation chain bearing weight. The reported parameter dependences are direct numerical consequences of the assumed formula rather than circular reductions. Concerns that Eq. (27) is not derived from the charged-particle action or not benchmarked against the Reissner-Nordström limit are validity/correctness critiques, not circularity. Similarly, the Euler-Heisenberg section's internal contradiction (Fig. 6 shows S_E decreasing with a, while Sec. IV says it increases) is an inconsistency, not a circular step. Accordingly, no specific circular step can be exhibited, and the circularity score is 0.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The paper introduces no new entities. Its quantitative claims rest on several hand-chosen parameters (m, q, and the scanned nonlinearity parameters), on unstated numerical inputs (l, G, M), and on an unproven Euclidean-action prescription that is effectively an additional assumption specific to this paper. The model metrics and the thermodynamic first law are standard inputs from the cited literature.

free parameters (5)
  • test particle mass m = 0.0002 (units unspecified)
    Chosen by hand for all numerical plots; the depth and shape of V_eff, and therefore the Euclidean action, depend on m through the (qΦ/m)^2 term.
  • test particle charge q = 0.005 (units unspecified)
    Chosen by hand alongside m; together they fix the scale of the effective potential and the computed tunneling probability.
  • nonlinearity parameters b, η, a, β = varied over ranges (e.g., b=0.02-0.18, η=0.1-0.9, a=0.1-0.5, β=1-500)
    These are model parameters inherited from the NLED Lagrangians, not fitted to data, but they are scanned by hand and the paper's main claims are statements about how the action depends on them.
  • AdS length l and Newton constant G = not stated
    Required to solve f(r_+)=0 for the black-hole mass M and to locate the turning point r_2; without them the numerical Euclidean action is undefined.
  • black hole mass M = implicit through r_+
    Determined by f(r_+)=0 for each horizon radius, but because l and G are unspecified, the relation between M, r_+, and the plotted quantities is not reproducible.
axioms (5)
  • domain assumption The isentropic condition for a charged particle reduces to E - qΦ = 0 (Eq. 12).
    This uses the first law T dS = dM - Φ dQ and identifies dM with the particle energy E and dQ with its charge q. The identification is nontrivial because it ignores possible gravitational binding energy and backreaction.
  • domain assumption The quantum transition amplitude is dominated by a Wick-rotated saddle point and Γ ≈ e^{-2S_E} (Eqs. 19-23).
    Standard WKB/semiclassical tunneling assumption applied to a single particle in a fixed black-hole background; backreaction and multi-particle effects are neglected.
  • ad hoc to paper The Euclidean action is S_E = ∫_{r2}^{r+} dr / sqrt(V_eff) (Eq. 27).
    This is the central quantitative formula. It is asserted without deriving L_E from the original charged-particle action, and its sign/normalization are not tested against any analytic limit, so the entire tunneling probability depends on an unproven prescription.
  • domain assumption For each of the four models, dV_eff/dr|_{r_+} = 4πT > 0.
    The paper states this is 'easily verified' for each model but does not give the explicit derivative computations; this positivity is what makes the process classically forbidden.
  • domain assumption The four NLED black-hole metrics and potentials from Refs. [32-37] are correct.
    The paper imports all spacetime and electromagnetic-potential structures from prior literature without re-deriving them.

pith-pipeline@v1.3.0-alltime-deepseek · 12975 in / 16424 out tokens · 174593 ms · 2026-08-03T09:25:44.580882+00:00 · methodology

0 comments
read the original abstract

We study the isentropic processes in a class of Anti de Sitter black holes coupled to non-linear electrodynamics. We demonstrate that such processes are classically forbidden but can proceed via quantum mechanical tunnelling. We compute the Euclidean action associated with the tunnelling process and analyze its dependence on the black hole charge, horizon radius, and the non-linear electrodynamics parameters characterizing each model. We find that the tunnelling probability is increasingly suppressed as the strength of the non-linearity is enhanced. We further find that smaller black holes exhibit a significantly higher tunnelling probability compared to larger ones, indicating a departure from classical behaviour. We conjecture that this behaviour may be universal across a broad class of black hole spacetimes. We discuss the implications of our results for entropy bounds and their potential relevance to the black hole information loss paradox.

Figures

Figures reproduced from arXiv: 2601.13786 by Mozib Bin Awal, Prabwal Phukon.

Figure 1
Figure 1. Figure 1: FIG. 1: Effective potential experienced by the charged test particle for an isentropic absorption by NED [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The plots presented above depict the Euclidean action associated with the isentropic absorption of [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Effective potential experienced by the charged test particle for an isentropic absorption by [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The plots presented above depict the Euclidean action associated with the isentropic absorption of [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Effective potential experienced by the charged test particle for an isentropic absorption by [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: The plots presented above depict the Euclidean action associated with the isentropic absorption of [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Effective potential experienced by the charged test particle for an isentropic absorption by [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: The plots presented above depict the Euclidean action associated with the isentropic absorption of [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

40 extracted references · 2 canonical work pages

  1. [1]

    Particle Creation by Black Holes,

    S. W. Hawking, “Particle Creation by Black Holes,” Commun. Math. Phys.43(1975), 199-220 [erratum: Com- mun. Math. Phys.46(1976), 206] doi:10.1007/BF02345020

    doi:10.1007/bf02345020 1975

  2. [2]

    Breakdown of Predictability in Gravitational Collapse,

    S. W. Hawking, “Breakdown of Predictability in Gravitational Collapse,” Phys. Rev. D14, 2460-2473 (1976)

    1976

  3. [3]

    Semi-classical black holes with large N re-scaling and information loss problem,

    D. Yeom and H. Zoe, “Semi-classical black holes with large N re-scaling and information loss problem,” Int. J. Mod. Phys. A26, 3287-3314 (2011) [arXiv:0907.0677 [hep-th]]

    Pith/arXiv arXiv 2011

  4. [4]

    Black Holes: Complementarity or Firewalls?,

    A. Almheiri, D. Marolf, J. Polchinski and J. Sully, “Black Holes: Complementarity or Firewalls?,” JHEP02, 062 (2013) [arXiv:1207.3123 [hep-th]]

    Pith/arXiv arXiv 2013

  5. [5]

    The LargeNlimit of superconformal field theories and supergravity,

    J. M. Maldacena, “The LargeNlimit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys.2, 231-252 (1998) [arXiv:hep-th/9711200 [hep-th]]

    Pith/arXiv arXiv 1998

  6. [6]

    Difficulties for the Evolution of Pure States Into Mixed States,

    T. Banks, L. Susskind and M. E. Peskin, “Difficulties for the Evolution of Pure States Into Mixed States,” Nucl. Phys. B244, 125-134 (1984)

    1984

  7. [7]

    Summary of Parallel Session: Black Hole Evaporation and Information Loss Paradox,

    Y . C. Ong and D. Yeom, “Summary of Parallel Session: Black Hole Evaporation and Information Loss Paradox,” Proceedings of the 2nd LeCosPA Symposium [arXiv:1602.06600 [hep-th]]

    Pith/arXiv arXiv

  8. [8]

    Black holes and entropy,

    J. D. Bekenstein, “Black holes and entropy,” Phys. Rev. D7, 2333-2346 (1973)

    1973

  9. [9]

    Some properties of Noether charge and a proposal for dynamical black hole entropy,

    V . Iyer and R. M. Wald, “Some properties of Noether charge and a proposal for dynamical black hole entropy,” Phys. Rev. D50, 846-864 (1994) [arXiv:gr-qc/9403028 [gr-qc]]

    Pith/arXiv arXiv 1994

  10. [10]

    Generalized second law of thermodynamics in black hole physics,

    J. D. Bekenstein, “Generalized second law of thermodynamics in black hole physics,” Phys. Rev. D9, 3292-3300 (1974) doi:10.1103/PhysRevD.9.3292

    doi:10.1103/physrevd.9.3292 1974

  11. [11]

    Black holes and entropy,

    J. D. Bekenstein, “Black holes and entropy,” Phys. Rev. D7(1973), 2333-2346 doi:10.1103/PhysRevD.7.2333

    doi:10.1103/physrevd.7.2333 1973

  12. [12]

    Black holes and the second law,

    J. D. Bekenstein, “Black holes and the second law,” Lett. Nuovo Cim.4, 737-740 (1972) doi:10.1007/BF02757029

    doi:10.1007/bf02757029 1972

  13. [13]

    A Universal Upper Bound on the Entropy to Energy Ratio for Bounded Systems,

    J. D. Bekenstein, “A Universal Upper Bound on the Entropy to Energy Ratio for Bounded Systems,” Phys. Rev. D23(1981), 287 doi:10.1103/PhysRevD.23.287

    doi:10.1103/physrevd.23.287 1981

  14. [14]

    What exactly does Bekenstein bound?,

    P. Hayden and J. Wang, “What exactly does Bekenstein bound?,” Quantum9(2025), 1664 doi:10.22331/q-2025- 03-20-1664 [arXiv:2309.07436 [hep-th]]

    Pith/arXiv arXiv 2025

  15. [15]

    Bound states and the Bekenstein bound,

    R. Bousso, “Bound states and the Bekenstein bound,” JHEP02(2004), 025 doi:10.1088/1126-6708/2004/02/025 17 [arXiv:hep-th/0310148 [hep-th]]

    Pith/arXiv arXiv 2004

  16. [16]

    A proof of the Bekenstein bound for any strength of gravity through holography,

    A. Pesci, “A proof of the Bekenstein bound for any strength of gravity through holography,” Class. Quant. Grav. 27(2010), 165006 doi:10.1088/0264-9381/27/16/165006 [arXiv:0903.0319 [gr-qc]]

    Pith/arXiv arXiv 2010

  17. [17]

    A Causal entropy bound,

    R. Brustein and G. Veneziano, “A Causal entropy bound,” Phys. Rev. Lett.84(2000), 5695-5698 doi:10.1103/PhysRevLett.84.5695 [arXiv:hep-th/9912055 [hep-th]]

    Pith/arXiv arXiv 2000

  18. [18]

    Acceleration Radiation and Generalized Second Law of Thermodynamics,

    W. G. Unruh and R. M. Wald, “Acceleration Radiation and Generalized Second Law of Thermodynamics,” Phys. Rev. D25(1982), 942-958 doi:10.1103/PhysRevD.25.942

    work page doi:10.1103/physrevd.25.942 1982

  19. [19]

    Entropy bounds, acceleration radiation, and the generalized second law

    W. G. Unruh and R. M. Wald, “Entropy bounds, acceleration radiation, and the generalized second law” Phys. Rev. D27(1983), 2271-2276 doi:10.1103/PhysRevD.27.2271

    work page doi:10.1103/physrevd.27.2271 1983

  20. [20]

    Bekenstein bound and uncertainty relations,

    L. Buoninfante, G. G. Luciano, L. Petruzziello and F. Scardigli, “Bekenstein bound and uncertainty relations,” Phys. Lett. B824(2022), 136818 doi:10.1016/j.physletb.2021.136818 [arXiv:2009.12530 [hep-th]]

    arXiv 2022

  21. [21]

    Covariant entropy bound beyond general relativity,

    T. Matsuda and S. Mukohyama, “Covariant entropy bound beyond general relativity,” Phys. Rev. D103(2021) no.2, 024002 doi:10.1103/PhysRevD.103.024002 [arXiv:2007.14015 [hep-th]]

    Pith/arXiv arXiv 2021

  22. [22]

    A Covariant entropy conjecture,

    R. Bousso, “A Covariant entropy conjecture,” JHEP07(1999), 004 doi:10.1088/1126-6708/1999/07/004 [arXiv:hep-th/9905177 [hep-th]]

    Pith/arXiv arXiv 1999

  23. [23]

    Generalized covariant entropy bound in Einstein gravity with quadratic curvature correc- tions,

    H. Zhu and J. Jiang, “Generalized covariant entropy bound in Einstein gravity with quadratic curvature correc- tions,” JHEP05(2024), 286 doi:10.1007/JHEP05(2024)286 [arXiv:2311.05352 [gr-qc]]

    Pith/arXiv arXiv 2024

  24. [24]

    Proof of classical versions of the Bousso entropy bound and of the generalized second law,

    E. E. Flanagan, D. Marolf and R. M. Wald, “Proof of classical versions of the Bousso entropy bound and of the generalized second law,” Phys. Rev. D62(2000), 084035 doi:10.1103/PhysRevD.62.084035 [arXiv:hep- th/9908070 [hep-th]]

    arXiv 2000

  25. [25]

    Bekenstein bound from the Pauli principle: a brief introduction,

    G. Acquaviva, A. Iorio and L. Smaldone, “Bekenstein bound from the Pauli principle: a brief introduction,” PoS ICHEP2020, 681 (2021) doi:10.22323/1.390.0681 [arXiv:2011.05176 [hep-th]]

    Pith/arXiv arXiv 2021

  26. [26]

    Bekenstein-Hawking Entropy and Strange Metals,

    S. Sachdev, “Bekenstein-Hawking Entropy and Strange Metals,” Phys. Rev. X5, no.4, 041025 (2015) doi:10.1103/PhysRevX.5.041025 [arXiv:1506.05111 [hep-th]]

    Pith/arXiv arXiv 2015

  27. [27]

    Remarks on the Sachdev-Ye-Kitaev model,

    J. Maldacena and D. Stanford, “Remarks on the Sachdev-Ye-Kitaev model,” Phys. Rev. D94, no.10, 106002 (2016) doi:10.1103/PhysRevD.94.106002 [arXiv:1604.07818 [hep-th]]

    Pith/arXiv arXiv 2016

  28. [28]

    Quasiparticle picture from the Bekenstein bound,

    G. Acquaviva, A. Iorio and M. Scholtz, “Quasiparticle picture from the Bekenstein bound,” PoSCORFU2017, 206 (2017) doi:10.22323/1.318.0206 [arXiv:1712.05275 [hep-th]]

    Pith/arXiv arXiv 2017

  29. [29]

    Entropy bounds and black hole remnants,

    J. D. Bekenstein, “Entropy bounds and black hole remnants,” Phys. Rev. D49, 1912-1921 (1994) doi:10.1103/PhysRevD.49.1912 [arXiv:gr-qc/9307035 [gr-qc]]

    Pith/arXiv arXiv 1912

  30. [30]

    Isentropic process of Reissner-Nordstr ¨om black holes: A possible excess of the entropy bound via a nonperturbative channel,

    R. B. Mann and D. h. Yeom, “Isentropic process of Reissner-Nordstr ¨om black holes: A possible excess of the entropy bound via a nonperturbative channel,” Phys. Rev. D112, no.6, 064042 (2025) doi:10.1103/t9px-txyf [arXiv:2505.01663 [gr-qc]]

    Pith/arXiv arXiv 2025

  31. [31]

    Isentropic processes for axisymmetric black holes,

    N. K. Dubey and S. Kolekar, “Isentropic processes for axisymmetric black holes,” Phys. Rev. D112, no.8, 084018 (2025) doi:10.1103/731x-38lt [arXiv:2507.08547 [gr-qc]]

    arXiv 2025

  32. [32]

    NED-AdS black holes, extended phase space thermodynamics and Joule–Thomson expansion,

    S. I. Kruglov, “NED-AdS black holes, extended phase space thermodynamics and Joule–Thomson expansion,” Nucl. Phys. B984, 115949 (2022) doi:10.1016/j.nuclphysb.2022.115949 [arXiv:2209.10524 [physics.gen-ph]]

    arXiv 2022

  33. [33]

    Regular magnetic black holes and monopoles from nonlinear electrodynamics,

    K. A. Bronnikov, “Regular magnetic black holes and monopoles from nonlinear electrodynamics,” Phys. Rev. D63, 044005 (2001) doi:10.1103/PhysRevD.63.044005 [arXiv:gr-qc/0006014 [gr-qc]]

    Pith/arXiv arXiv 2001

  34. [34]

    Thermodynamics and phase transition of anti de Sitter black holes with ModMax nonlinear electrodynamics and perfect fluid dark matter,

    Y . Sekhmani, S. K. Maurya, M. K. Jasim, ˙I. Sakallı, J. Rayimbaev and I. Ibragimov, “Thermodynamics and phase transition of anti de Sitter black holes with ModMax nonlinear electrodynamics and perfect fluid dark matter,” Eur. Phys. J. C85(2025) no.3, 229 doi:10.1140/epjc/s10052-025-13932-5

    doi:10.1140/epjc/s10052-025-13932-5 2025

  35. [35]

    LECTURES ON NON LINEAR ELECTRODYNAMICS,

    J. Plebanski, “LECTURES ON NON LINEAR ELECTRODYNAMICS,” RX-476

  36. [36]

    Duality Rotations and TypeDSolutions to Einstein Equations With Nonlinear Electromagnetic Sources,

    I. H. Salazar, A. Garcia and J. Plebanski, “Duality Rotations and TypeDSolutions to Einstein Equations With Nonlinear Electromagnetic Sources,” J. Math. Phys.28(1987), 2171-2181 doi:10.1063/1.527430

    doi:10.1063/1.527430 1987

  37. [37]

    Foundations of the new field theory,

    M. Born and L. Infeld, “Foundations of the new field theory,” Proc. Roy. Soc. Lond. A144(1934) no.852, 425-451 doi:10.1098/rspa.1934.0059

    arXiv 1934

  38. [38]

    Lessons from the information paradox,

    S. Raju, “Lessons from the information paradox,” Phys. Rept.943(2022), 1-80 doi:10.1016/j.physrep.2021.10.001 [arXiv:2012.05770 [hep-th]]

    Pith/arXiv arXiv 2022

  39. [39]

    The Page curve of Hawking radiation from semiclassical geometry,

    A. Almheiri, R. Mahajan, J. Maldacena and Y . Zhao, “The Page curve of Hawking radiation from semiclassical geometry,” JHEP03(2020), 149 doi:10.1007/JHEP03(2020)149 [arXiv:1908.10996 [hep-th]]

    Pith/arXiv arXiv 2020

  40. [40]

    Observations of Hawking radiation: the Page curve and baby universes,

    D. Marolf and H. Maxfield, “Observations of Hawking radiation: the Page curve and baby universes,” JHEP04 (2021), 272 doi:10.1007/JHEP04(2021)272 [arXiv:2010.06602 [hep-th]]

    Pith/arXiv arXiv 2021