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On the nature of the black hole information problem

T0 review · 0 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This review argues that the black hole information problem is a conjunction of five semiclassical assumptions, and that complete evaporation under those assumptions genuinely predicts pure-to-mixed information loss.

desk verdict A careful, honest master's-thesis-style review of the information problem; no new results, but the assumption-tracking and derivations are sound. read the letter →

arxiv 2505.17220 v1 pith:KGHNF5O7 submitted 2025-05-22 gr-qc hep-thmath-phmath.MP

Thiago T. Bergamaschi This is my paper · ORCID
classification gr-qchep-thmath-phmath.MP MSC 83C5783C4781T2083C75 PACS 04.70.Dy04.62.+v
keywords blackholeinformationproblemsemiclassicalgravityHawkingradiationevaporationquantumfieldtheoryincurvedspacetimeuniquenesstheoremscosmiccensorshipconjectureHadamardstates
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

The paper aims to show that the black hole information problem is constituted by a list of assumptions rather than by a single theorem. Under the semiclassical picture, a pure state that collapses into a black hole ends, after complete evaporation, in a mixed state of radiation; this is information loss. The paper argues that the conclusion follows if five premises hold: cosmic censorship, the stationary-state conjecture that a formed black hole is characterized only by its mass, angular momentum, and charge, the Hadamard condition for physically acceptable states, complete evaporation through the Planck scale, and the absence of alternatives to unitarity. If true, the information problem is a genuine prediction of semiclassical gravity, and resolving it means saying which assumption breaks.

What carries the argument

The central mechanism is the Hawking particle-creation calculation on a fixed curved background. In collapse, the vacuum associated with late-time observers differs from the vacuum of the initial configuration, producing an approximately thermal flux of outgoing radiation from the horizon. Entanglement between modes inside and outside the horizon is then an intrinsic feature of quantum field theory in curved spacetime; when the black hole evaporates completely, tracing over the interior degrees of freedom converts the initially pure state into a mixed state. The paper's analytic machinery is the resulting assumption-list, which makes explicit where each of these steps enters the argument.

What would settle it

Compute the entropy of the Hawking radiation through the full evaporation in a model that includes backreaction; if the entanglement entropy rises to a thermal maximum and then decreases back to zero, the semiclassical pure-to-mixed prediction is false. A stable Planck-mass remnant appearing after the expected evaporation time would likewise falsify the complete-evaporation assumption.

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Extended reading notes

Core claim

The central claim is that the formation and complete evaporation of a black hole, as described by semiclassical gravity, leads to information loss: an initial pure state inevitably evolves into a mixed state. That conclusion is not delivered by a single theorem; it is assembled from a conjunction of hypotheses, each of which can in principle fail. The paper therefore formulates the black hole information problem as a question about the final state of an evaporating black hole, conditioned on cosmic censorship, the stationary-state conjecture, Hadamard states, complete evaporation, and no alternatives to unitarity. The author's conclusion is that information loss is what semiclassical gravity predicts, and the problem dissolves only if at least one listed assumption fails.

Load-bearing premise

The load-bearing premise is that the semiclassical description remains valid through the entire evaporation, including the final Planck-scale stages, so the black hole evaporates completely and leaves only radiation.

Editorial extensions

If this is right

  • Information loss is a genuine semiclassical prediction, not a paradox read into the formalism: as long as all five assumptions hold, the pure-to-mixed transition follows.
  • The problem cannot be resolved by a single mechanism alone; any resolution must identify which of the five assumptions fails, and where.
  • If one assumption fails, such as complete evaporation being replaced by a remnant or a final-state boundary, the argument for information loss collapses even if Hawking radiation is unchanged.
  • Quantum gravity must supply the missing information bookkeeping across the Planck scale; evaporation is the natural arena where unitarity and semiclassical gravity are tested.
  • Black hole thermodynamics and the uniqueness theorems are load-bearing: without the stationary-state conjecture, the black hole need not be characterized by $(M,L,q)$, so the loss of details cannot even be formulated.

Reading between the lines

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

  • Beyond the paper: the five-assumption list can serve as a classification key for proposed resolutions; each candidate solution targets one assumption, such as remnants targeting complete evaporation, final-state proposals targeting the absence of a boundary, and modified quantum field theory targeting Hadamard states.
  • Beyond the paper: the same deconstruction could be applied to other semiclassical information puzzles, asking which assumptions must be abandoned before a pure-to-mixed transition is inferred.
  • Beyond the paper: a numerical toy model of evaporation with backreaction could test the weakest assumption directly; if the late-time entanglement entropy of the radiation turns over and drops back to zero, the complete-evaporation premise is undermined even before quantum gravity is included.
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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

0 major / 5 minor

Summary. The manuscript, based on a master's dissertation, reviews the classical and semiclassical foundations of black hole physics and formulates the black hole information problem as a conditional consequence of semiclassical gravity. It surveys Lorentzian geometry, causal structure, energy conditions, singularities, asymptotic flatness, the Schwarzschild and Kerr spacetimes, black hole thermodynamics, quantum field theory in curved spacetime, the Hawking effect, and quantum information, and then argues that if the semiclassical picture remains valid through complete evaporation, an initial pure state evolves to a mixed state. The paper explicitly identifies the assumptions involved (cosmic censorship, the stationary state conjecture, the Hadamard condition, complete evaporation, and the absence of alternatives to unitarity) and states that the information-loss prediction is conditional on no deviations from the semiclassical picture at the Planck scale.

Significance. As a review, the paper is careful and largely self-contained. The derivations I checked match standard references: the Raychaudhuri equation (2.4.14), the Kretschmann scalar (3.1.3), the surface gravity (3.4.19), and the Smarr formula (3.5.49). The central thesis is honestly qualified: the information-loss conclusion is presented as conditional on the validity of the semiclassical description up to the endpoint of evaporation, with Figure 29 and the surrounding text marking where semiclassical gravity is expected to fail. The paper introduces no free parameters and no ad hoc entities, and it is explicit about which inputs are conjectures rather than theorems. Its main value is a systematic and readable statement of the assumption structure behind the information problem, although it does not offer a new resolution or a formal proof of the sufficiency of the listed assumptions.

minor comments (5)
  1. [§3.1] In the text near eq. (3.1.1), the phrase 'an spherically symmetric distribution' should read 'a spherically symmetric distribution'.
  2. [§3.4] In the sentence before eq. (3.4.19), 'Schwarschild' is a typo and should be 'Schwarzschild'.
  3. [§5.2] The discussion of alternatives to information loss is quite brief and does not mention the recent Page-curve and island/replica-wormhole literature; even a short pointer to these developments would help readers connect the review to current research.
  4. [Appendix C] The title 'Von Neumann entropy' should use a lowercase 'v' in 'von Neumann' to match standard usage.
  5. [§3.5] The unit system is not always stated explicitly when equations are written; for example, eq. (3.5.29) is presented without a reminder of whether geometrized or SI units are in force, and a brief note at the start of the chapter would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the information-loss claim is explicitly conditional on unproven semiclassical complete evaporation, and all load-bearing assumptions are flagged as conjectures or imported standard results.

full rationale

The paper is a pedagogical review whose central claim is a conditional: if the semiclassical picture holds through complete evaporation, then an initially pure state evolves to a mixed state. This conditionality is stated in the abstract ('Conscious that such a prediction follows if no deviations from the semiclassical picture occur at the Planck scale') and in section 1 ('such a prediction of information loss follows from the expectation that the evaporation process occurs completely'), with Figure 29 later marking where semiclassical gravity is expected to fail. The conclusion is therefore an explicit entailment of the stated assumptions, not a quantity fitted to data or defined in terms of itself. The other load-bearing premises—cosmic censorship, the stationary state conjecture, and the Hadamard condition—are presented as conjectures or conditions taken from the prior literature, not derived from the target conclusion. The black-hole uniqueness theorems are cited as standard external results and are not used to forbid alternatives to unitarity. No parameter is fitted and renamed as a prediction, and no self-citation chain supplies the argument. The derivation is self-contained as a review, with its limitations explicitly acknowledged, so no significant circularity is present.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

This is a review, so the ledger measures what the exposition imports rather than what it introduces. No free parameters are fitted anywhere in the text, and no new entities are postulated. The axiomatic load is carried by standard semiclassical gravity assumptions, and notably every one of them is explicitly named as an assumption or conjecture in the paper, which is good practice for a review of this kind.

assumptions (6)
  • domain assumption Cosmic censorship conjecture (weak form): all physical spacetimes are globally hyperbolic, so naked singularities do not arise from gravitational collapse.
    Invoked in section 3.2 to define strongly asymptotically predictable spacetimes and the black hole region B = M \ psi^{-1}[J^-(I^+)]. The paper states it explicitly as a conjecture, so it is flagged rather than hidden.
  • domain assumption Stationary state conjecture: after sufficiently late times a formed black hole settles to a stationary metric, so the no-hair description by (M, L, q) applies.
    Stated in section 3.5 and needed for the pure-to-mixed transition argument in section 5.1. The paper identifies it as a conjecture with no proof.
  • domain assumption Hadamard condition selects the physically acceptable states in quantum field theory in curved spacetime.
    Used in section 4.4 to establish that entanglement between causally complementary regions is an intrinsic feature of QFT, a step in the information-loss argument. Stated as an assumption in the chapter 4 overview.
  • domain assumption Null energy condition (derived from the weak or strong energy conditions) holds for the classical matter content used in the focusing and area theorems.
    Used in propositions 2.4.2, 3.2.2, 3.2.3 and theorem 3.3.1. The author notes in section 2.3 that such conditions are classical expectations that can fail in quantum theory.
  • domain assumption The null geodesic generators of the event horizon are future complete; no singularity develops on the horizon itself.
    Theorem 3.3.1 (area theorem) requires this completeness, as the author explicitly notes: the generators must be complete or the focusing argument breaks.
  • domain assumption Black hole uniqueness theorems: stationary Einstein-Maxwell black holes are described by the Kerr-Newman metric and characterized only by (M, L, q).
    Relied on in sections 3.5 and 5.1 as established background, citing references 20 and 66. This is a cited theorem rather than a new derivation, and the paper depends on it for the no-hair step.

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Cite this review

Pith. "Pith review of On the nature of the black hole information problem." pith.science (2026). https://pith.science/paper/KGHNF5O7

@misc{pith2026250517220,
  author       = {Pith},
  title        = {Pith review of: On the nature of the black hole information problem},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KGHNF5O7}},
  note         = {Machine review of arXiv:2505.17220}
}
read the original abstract

The aim of this work is to present the black hole information problem and discuss the assumptions and hypotheses necessary for its formulation. As the problem arises in the framework of semiclassical gravity, we first review the necessary notions to describe Lorentzian manifolds equipped with physical properties, as well as the physical concepts of the theory that describes the gravitational interaction as the curvature of spacetime, general relativity. From its classical perspective, we develop the formalism to study the dynamical aspects of black holes in spacetimes obeying suitable causality conditions. Equipped with conjectures that nature censors naked singularities and that black holes reach a stationary configuration after they form, the black hole uniqueness theorems allow us to review several relations for the geometrical quantities associated with them. Following considerations of the other fundamental interactions, which are described by quantum field theory, we review the arguments in the formalism of quantum field theory in curved spacetime that give rise to the effective particle creation effect, its approximately thermal character, and the concept of black hole evaporation. With a precise quantification of information in quantum mechanics and assuming that the condition for physically acceptable states is given by the Hadamard condition, we review the result that entanglement between causally complementary regions is an intrinsic feature of quantum field theory. As a consequence, we discuss how the formation and complete evaporation of black holes leads to information loss. Conscious that such a prediction follows if no deviations from the semiclassical picture occur at the Planck scale, we discuss alternatives to this nonunitary dynamical evolution and formulate the black hole information problem. Lastly, we analyze the assumptions and hypotheses that lead to the problem.

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Works this paper leans on

15 extracted references · 5 canonical work pages

  1. [4]

    Accessible at: 28 Mar

    Available at: https://link.aps.org/doi/10.1103/PhysRevD.7.2850. Accessible at: 28 Mar. 2024. 147 29 DAVIES, P. C. W. Scalar production in Schwarzschild and Rindler metrics. Journal of Physics A, v. 8, n. 4, p. 609, Apr. 1975. Available at: https: //dx.doi.org/10.1088/0305-4470/8/4/022. Accessible at: 28 Mar. 2024. 30 UNRUH, W. G. Notes on black-hole evapo...

    doi:10.1103/physrevd.7.2850 2024

  2. [8]

    Accessible at: 28 Mar

    Available at: https://doi.org/10.1007/BF01221129. Accessible at: 28 Mar. 2024. 150 73 SULLIVAN, B.; ISRAEL, W. The third law of black hole mechanics: what is it? Physics Letters A, v. 79, n. 5, p. 371–372, 1980. Available at: https: //doi.org/10.1016/0375-9601(80)90266-2. Accessible at: 28 Mar. 2024. 74 ISRAEL, W. Third law of black-hole dynamics: A formu...

    work page doi:10.1007/bf01221129 2024

  3. [16]

    Emergent Gravity in a Holographic Universe

    Accessible at: Mar. 3th 2024. 163 VISSER, M. R. Emergent gravity in a holographic universe. 2019. Thesis (Doctorate) — University of Amsterdam, 2019. Available at: https: //doi.org/10.48550/arXiv.1908.05469. Accessible at: Mar. 4th 2024. 164 MALDACENA, J. The large-N limit of superconformal field theories and supergravity.International Journal of Theoreti...

    work page Pith review arXiv doi:10.48550/arxiv.1908.05469 2024

  4. [1963]

    Accessible at: 28 Mar

    Available at: https://link.aps.org/doi/10.1103/PhysRev.129.1873. Accessible at: 28 Mar. 2024. 47 PENROSE, R. Techniques of differential topology in relativity. Philadelphia: SIAM, 1972. 48 GEROCH, R. Domain of dependence.Journal of Mathematical Physics, v. 11, n. 2, p. 437–449, Feb. 1970. Available at: https://doi.org/10.1063/1.1665157. Accessible at: 28 ...

    doi:10.1103/physrev.129.1873 2024

  5. [1973]

    Accessible at: 28 Mar

    Available at: https://doi.org/10.1007/BF01645742. Accessible at: 28 Mar. 2024. 20 HEUSLER, M. Black hole uniqueness theorems. Cambridge: Cambridge University Press, 1996. 21 BEKENSTEIN, J. D. Black holes and the second law.Lettere al Nuovo Cimento, v. 4, n. 15, p. 737–740, June 1972. Available at: https://doi.org/10.1007/BF02757029. Accessible at: 28 Mar....

    doi:10.1007/bf01645742 2024

  6. [1974]

    Accessible at: 28 Mar

    Available at: https://link.aps.org/doi/10.1103/PhysRevD.9.3292. Accessible at: 28 Mar. 2024. 89 BEKENSTEIN, J. D. Black-hole thermodynamics.Physics Today, v. 33, n. 1, p. 24–31, 1980. Available at: https://doi.org/10.1063/1.2913906. Accessible at: 28 Mar. 2024. 90 WALD, R. The thermodynamics of black holes.Living Reviews in Relativity, v. 4, n. 1, p. 6, J...

    arXiv doi:10.48550/arxiv.1208.5399 2013

  7. [1978]

    Available at: https://doi.org/10.1063/1.523863

    ISSN 0022-2488. Available at: https://doi.org/10.1063/1.523863. Accessible at: 28 Mar. 2024. 70 O’NEILL, B. The geometry of Kerr black holes. Wellesley: A K Peters, 1995. 71 CHRUŚCIEL, P. T.Geometry of black holes. Oxford: Oxford University Press, 2020. 72 FARRUGIA, C. J.; HÁJÍCEK, P. The third law of black hole mechanics: a counterexample. Communications...

    work page doi:10.1063/1.523863 2024

  8. [1979]

    p. 212–293. 50 GALLOWAY, G. J. Notes on Lorentzian causality. Available at: https: //www.math.miami.edu/~galloway/vienna-course-notes.pdf. Accessible at: 8 Feb. 2024. 51 POISSON, E. A relativist’s toolkit. Cambridge: Cambridge University Press, 2004. 52 MAGNUS, J. R.; NEUDECKER, H. Matrix differential calculus with applications in statistics and econometr...

    arXiv 2024

Show all 15 references
  1. [1994]

    Accessible at: 28 Mar

    Available at: https://dx.doi.org/10.1088/0264-9381/11/3/014. Accessible at: 28 Mar. 2024. 158 HAWKING, S. W.; PERRY, M. J.; STROMINGER, A. Soft hair on black holes. Physical Review Letters, American Physical Society, v. 116, p. 231301, June 2016. Available at: https://link.aps...

    2017 doi

  2. [1997]

    Accessible at: 28 Mar

    Available at: https://link.aps.org/doi/10.1103/PhysRevD.55.861. Accessible at: 28 Mar. 2024. 151 HOROWITZ, G. T. Quantum states of black holes.In: WALD, R. (ed.).Black holes and relativistic stars. Chicago: University of Chicago Press, 1998. p. 241–266. 152 HUBENY, V. E. The A...

    2024 doi

  3. [2010]

    v. 1. 26 PESKIN, M. E.; SCHROEDER, D. V.An introduction to quantum field theory. Boulder: Westview Press, 1995. (Frontiers in Physics). 27 FAN, X. et al.Measurement of the electron magnetic moment.Physical Review Letters, American Physical Society, v. 130, p. 071801, Feb. 2023...

    1995 doi

  4. [2011]

    175 LEITHOLD, L

    (Graduate Texts in Mathematics). 175 LEITHOLD, L. The calculus, with analytic geometry. 3rd ed. New York: Harper & Row, 1976. 158 176 GHORPADE, S. R.; LIMAYE, B. V.A course in calculus and real analysis. 1st ed. New York: Springer, 2006. (Undergraduate texts in mathematics). 1...

    1976 doi arXiv

  5. [2012]

    183 HORODECKI, R

    (Springer series on atomic, optical, and plasma physics). 183 HORODECKI, R. et al. Quantum entanglement. Reviews of Modern Physics, American Physical Society, v. 81, p. 865–942, June 2009. Available at: https://link.aps.org/doi/10.1103/RevModPhys.81.865. 184 SCHRÖDINGER, E. Di...

    2009 doi

  6. [2016]

    Accessible at: 28 Mar

    Available at: https://link.aps.org/doi/10.1103/PhysRevLett.116.061102. Accessible at: 28 Mar. 2024. 8 OPPENHEIMER, J. R.; SNYDER, H. On continued gravitational contraction. Physical Review, American Physical Society, v. 56, p. 455–459, Sept. 1939. Available at: https://link.ap...

    2024

  7. [2017]

    connected

    Available at: https://doi.org/10.1038/nature23675. Accessible at: 28 Mar. 2024. Appendix 161 APPENDIX A – MANIFOLDS The purpose of this appendix is to provide an objective review of the basic mathe- matical framework necessary for the development of this work. We start by pres...

    2024 doi

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