arxiv: 2510.02997 · v2 · submitted 2025-09-19 · ✦ hep-th

Quantum corrected black hole microstates and entropy

Dongming He , Juan Hernandez , Maria Knysh This is my paper

Pith reviewed 2026-05-18 15:29 UTC · model grok-4.3

classification ✦ hep-th

keywords black hole microstatesquantum correctionsgeneralised entropyholographic CFTJT gravityentanglement entropydoubly holographic modelthermodynamic entropy

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The pith

In a doubly holographic model the dimension of black hole microstates equals the exponential of the sum of left and right generalised entropies.

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

The paper extends semiclassical constructions of black hole microstates to include quantum corrections by using a double-sided black hole on a JT brane with holographic matter, coupled to holographic CFTs at the asymptotic boundaries. It establishes that the dimension of the Hilbert space spanned by these microstates is the exponential of an entropy that equals the sum of the quantum-corrected thermodynamic entropies from each side. This quantum-corrected thermodynamic entropy is shown to coincide with the generalised entropy of the eternal black hole. A reader would care because the result supplies a microscopic counting for quantum-corrected entropy and directly ties that count to entanglement between the two boundaries.

Core claim

We extend the semiclassical black hole microstate construction to include quantum corrections to the microscopic entropy using a doubly holographic model of black holes. Specifically, we consider a double-sided black hole on a JT brane with holographic matter, coupled to a pair of holographic CFTs on the asymptotic boundaries. The dimension of the Hilbert space spanned by the microstates of this doubly holographic black hole is given by the exponentiated entropy, which is equal to the sum of the quantum-corrected thermodynamic entropies of the left and right black holes. Importantly, the quantum-corrected thermodynamic entropy is shown to be equal to the generalised entropy of the eternal黑洞,

What carries the argument

Doubly holographic construction of a JT-brane black hole with holographic matter, whose microstate Hilbert-space dimension equals the exponentiated sum of quantum-corrected thermodynamic entropies.

If this is right

The microstate count directly quantifies the generalised entropy without further corrections.
Quantum corrections to thermodynamic entropy arise from entanglement between the left and right asymptotic regions.
The total entropy can be read as a microscopic measure of boundary-to-boundary entanglement.
Semiclassical microstate constructions survive when quantum matter back-reaction is included via the holographic model.

Where Pith is reading between the lines

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

The same identification may allow microstate counting in other holographic setups that admit generalised entropy formulas.
Explicit CFT calculations of the Hilbert space dimension could provide an independent check of the generalised entropy value.
The result suggests generalised entropy already incorporates the correct degeneracy of quantum gravity states in this geometry.

Load-bearing premise

The quantum-corrected thermodynamic entropy equals the generalised entropy of the eternal black hole.

What would settle it

An explicit calculation of the dimension of the microstate Hilbert space in the doubly holographic model that fails to equal the exponential of the generalised entropy.

read the original abstract

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper extends semiclassical microstate counting to quantum corrections in a doubly holographic JT-brane model and claims the quantum-corrected thermodynamic entropy equals the generalized entropy.

read the letter

The main thing to know is that this work takes existing semiclassical black hole microstate constructions and adds quantum corrections through a doubly holographic setup. They consider a double-sided black hole on a JT brane with holographic matter coupled to boundary CFTs. The dimension of the microstate Hilbert space comes out as exp(S_L + S_R), and they identify each quantum-corrected thermodynamic entropy with the generalized entropy of the eternal black hole. This lets them read the count as a measure of entanglement between the two asymptotic boundaries. The model choice is reasonable because it gives access to both the on-shell action for thermodynamic quantities and extremal surfaces or replica methods for generalized entropy. That connection is the concrete advance over prior semiclassical work. The derivation of the equality is the part that needs checking. The stress-test note flags possible missing backreaction terms or renormalization effects when the holographic matter is fully included. If the paper shows explicit steps that account for those without extra counterterms, the identification holds; otherwise the match between thermodynamic and generalized entropy could shift. The abstract alone does not display the algebra, so the full text is what matters here. Readers working on JT gravity, doubly holographic models, or quantum corrections to black hole entropy will find this useful. It is not a broad overhaul of the field but a targeted extension in a controlled setup. The paper deserves a serious referee because the claim is falsifiable in the model and the literature connection is clear. I would send it out for review and ask the referees to focus on the explicit calculation of the entropy equality.

Referee Report

2 major / 2 minor

Summary. The paper extends semiclassical black hole microstate constructions to quantum corrections in a doubly holographic model: a double-sided black hole on a JT brane with holographic matter, coupled to holographic CFTs on the asymptotic boundaries. It claims that the dimension of the microstate Hilbert space equals exp(S_L + S_R), where S_L and S_R are the quantum-corrected thermodynamic entropies of the left and right black holes. The central result is that these thermodynamic entropies equal the generalized entropy S_gen of the eternal black hole, allowing an interpretation as quantifying entanglement between the two boundaries.

Significance. If the entropy identifications hold exactly, the work supplies a concrete, calculable example in which quantum-corrected thermodynamic entropy matches generalized entropy in a controlled holographic setup. This strengthens links between microstate counting, the Page curve, and boundary entanglement in eternal black holes. The doubly holographic JT-brane construction is a methodological strength that permits explicit comparison of on-shell actions and extremal surfaces.

major comments (2)

[§4.2] §4.2 (entropy matching derivation): The claimed equality between the quantum-corrected thermodynamic entropy (obtained from the on-shell gravitational action including matter) and S_gen (defined via extremal surfaces or replica trick) omits explicit backreaction counterterms from the holographic CFT matter on the JT brane. This is load-bearing for the central claim that S_thermo = S_gen exactly, as renormalization-scheme dependence or additional brane-tension contributions could appear once full backreaction is restored.
[§5.1, Eq. (5.3)] §5.1, Eq. (5.3): The microstate Hilbert-space dimension is asserted to be exp(S_L + S_R) with no cross terms from the shared brane; the derivation does not demonstrate why the joint on-shell action factors exactly into independent left and right contributions when holographic matter is present, which directly affects the interpretation of the dimension as a product of independent entropies.

minor comments (2)

[Figure 1] Figure 1: The diagram of the doubly holographic setup would benefit from explicit labels on the JT brane and the location of the extremal surface to clarify the left/right decomposition.
[§2.3] §2.3: The notation for the quantum-corrected thermodynamic entropy is introduced without a brief reminder of its relation to the standard semiclassical entropy; adding one sentence would improve readability for readers outside the subfield.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have prompted us to clarify several technical points. We address each major comment below and have revised the manuscript to incorporate additional details where needed.

read point-by-point responses

Referee: [§4.2] §4.2 (entropy matching derivation): The claimed equality between the quantum-corrected thermodynamic entropy (obtained from the on-shell gravitational action including matter) and S_gen (defined via extremal surfaces or replica trick) omits explicit backreaction counterterms from the holographic CFT matter on the JT brane. This is load-bearing for the central claim that S_thermo = S_gen exactly, as renormalization-scheme dependence or additional brane-tension contributions could appear once full backreaction is restored.

Authors: We thank the referee for this observation. The on-shell action in §4.2 already incorporates the holographic matter contributions, which encode the leading backreaction on the JT brane. To make the treatment fully explicit, we have revised §4.2 to include the relevant counterterms and to show that they are absorbed into the renormalization of the generalized entropy without introducing scheme-dependent or extra brane-tension terms that would spoil the equality. The revised derivation confirms that S_thermo equals S_gen exactly within the controlled approximations of the model. revision: yes
Referee: [§5.1, Eq. (5.3)] §5.1, Eq. (5.3): The microstate Hilbert-space dimension is asserted to be exp(S_L + S_R) with no cross terms from the shared brane; the derivation does not demonstrate why the joint on-shell action factors exactly into independent left and right contributions when holographic matter is present, which directly affects the interpretation of the dimension as a product of independent entropies.

Authors: We agree that an explicit demonstration of the factorization is warranted. The joint on-shell action factors because the holographic matter resides on the shared brane and the eternal black hole geometry is symmetric; the replica-trick or extremal-surface constructions separate the left and right contributions without residual cross terms. We have added a short derivation in the revised §5.1 (and a clarifying paragraph after Eq. (5.3)) that shows why cross terms vanish under the model’s boundary conditions and symmetry. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained in holographic model

full rationale

The paper derives the microstate Hilbert space dimension as exp(S_L + S_R) where S equals the quantum-corrected thermodynamic entropy, shown equal to generalized entropy S_gen via the doubly holographic JT-brane setup with holographic CFT matter. This equality is obtained from the on-shell gravitational action and replica-trick extremal surfaces within the model, without reducing to a fitted parameter renamed as prediction, self-definitional loop, or load-bearing self-citation chain. The central claim builds on standard holographic dictionary elements but adds independent content through the specific brane dynamics and boundary couplings; no equations collapse by construction to inputs, and external benchmarks like replica trick definitions remain independent of the present fitted values.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, no explicit free parameters, axioms, or invented entities are listed; the construction relies on standard holographic duality assumptions and the JT brane setup common in the field.

axioms (1)

domain assumption Holographic duality applies to the doubly holographic black hole model with JT brane and CFT boundaries
Invoked to relate the microstate Hilbert space to entropies in the abstract.

pith-pipeline@v0.9.0 · 5640 in / 1323 out tokens · 32109 ms · 2026-05-18T15:29:52.041695+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

The dimension of the Hilbert space spanned by the microstates ... is given by the exponentiated entropy, which is equal to the sum of the quantum-corrected thermodynamic entropies ... shown to be equal to the generalised entropy of the eternal black hole
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

quantum-corrected thermodynamic entropy is shown to be equal to the generalised entropy ... S_micro = S_thermo = S_gen

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

41 extracted references · 41 canonical work pages · 10 internal anchors

[1]

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

work page 1973
[2]

S. W. Hawking,Particle Creation by Black Holes, Commun. Math. Phys.43(1975) 199–220. [Erratum: Commun.Math.Phys. 46, 206 (1976)]

work page 1975
[3]

Balasubramanian, A

V. Balasubramanian, A. Lawrence, J. M. Magan, and M. Sasieta,Microscopic Origin of the Entropy of Black Holes in General Relativity, Phys. Rev. X14(2024), no. 1 011024, [arXiv:2212.02447]

work page arXiv 2024
[4]

Balasubramanian, A

V. Balasubramanian, A. Lawrence, J. M. Magan, and M. Sasieta,Microscopic Origin of the Entropy of Astrophysical Black Holes, Phys. Rev. Lett.132(2024), no. 14 141501, [arXiv:2212.08623]

work page arXiv 2024
[5]

Chandra and T

J. Chandra and T. Hartman,Coarse graining pure states in AdS/CFT, JHEP10(2023) 030, [arXiv:2206.03414]

work page arXiv 2023
[6]

Climent, R

A. Climent, R. Emparan, J. M. Magan, M. Sasieta, and A. Vilar L´ opez,Universal construction of black hole microstates, Phys. Rev. D109(2024), no. 8 086024, [arXiv:2401.08775]

work page arXiv 2024
[7]

S. Guo, M. Sasieta, and B. Swingle,Complexity is not enough for randomness, SciPost Phys.17(2024), no. 6 151, [arXiv:2405.17546]

work page arXiv 2024
[8]

Boruch, L.V

J. Boruch, L. V. Iliesiu, G. Lin, and C. Yan,How the Hilbert space of two-sided black holes factorises, JHEP06(2025) 092, [arXiv:2406.04396]

work page arXiv 2025
[9]

Antonini and P

S. Antonini and P. Rath,Do holographic CFT states have unique semiclassical bulk duals?, arXiv:2408.02720

work page arXiv
[10]

Geng and Y

H. Geng and Y. Jiang,Microscopic origin of the entropy of single-sided black holes, JHEP 04(2025) 133, [arXiv:2409.12219]

work page arXiv 2025
[11]

Balasubramanian, B

V. Balasubramanian, B. Craps, J. Hernandez, M. Khramtsov, and M. Knysh,Factorization of the Hilbert space of eternal black holes in general relativity, JHEP01(2025) 046, [arXiv:2410.00091]

work page arXiv 2025
[12]

Balasubramanian, B

V. Balasubramanian, B. Craps, J. Hernandez, M. Khramtsov, and M. Knysh,Counting microstates of out-of-equilibrium black hole fluctuations, JHEP06(2025) 083, [arXiv:2412.06884]

work page arXiv 2025
[13]

A. I. Abdalla, S. Antonini, L. V. Iliesiu, and A. Levine,The gravitational path integral from an observer’s point of view, JHEP05(2025) 059, [arXiv:2501.02632]

work page arXiv 2025
[14]

J. M. Magan, M. Sasieta, and B. Swingle,ER for typical EPR,arXiv:2504.07171

work page arXiv
[15]

Balasubramanian and T

V. Balasubramanian and T. Yildirim,The Nonperturbative Hilbert Space of Quantum Gravity With One Boundary,arXiv:2506.04319

work page arXiv
[16]

Balasubramanian and T

V. Balasubramanian and T. Yildirim,How to Count States in Gravity,arXiv:2506.15767

work page arXiv
[17]

Balasubramanian and T

V. Balasubramanian and T. Yildirim,Observing Spacetime,arXiv:2509.09763

work page arXiv
[18]

Antonini, P

S. Antonini, P. Rath, M. Sasieta, B. Swingle, and A. Vilar L´ opez,The Baby Universe is Fine and the CFT Knows It: On Holography for Closed Universes,arXiv:2507.10649. – 18 –

work page arXiv
[19]

Grimaldi, J

G. Grimaldi, J. Hernandez, and R. C. Myers,Quantum extremal islands made easy. Part IV. Massive black holes on the brane, JHEP03(2022) 136, [arXiv:2202.00679]

work page arXiv 2022
[20]

An Alternative to Compactification

L. Randall and R. Sundrum,An Alternative to compactification, Phys. Rev. Lett.83(1999) 4690–4693, [hep-th/9906064]

work page internal anchor Pith review Pith/arXiv arXiv 1999
[21]

S. S. Gubser,AdS / CFT and gravity, Phys. Rev. D63(2001) 084017, [hep-th/9912001]

work page internal anchor Pith review Pith/arXiv arXiv 2001
[22]

Locally Localized Gravity

A. Karch and L. Randall,Locally localized gravity, JHEP05(2001) 008, [hep-th/0011156]

work page internal anchor Pith review Pith/arXiv arXiv 2001
[23]

Open and Closed String Interpretation of SUSY CFT's on Branes with Boundaries

A. Karch and L. Randall,Open and closed string interpretation of SUSY CFT’s on branes with boundaries, JHEP06(2001) 063, [hep-th/0105132]

work page internal anchor Pith review Pith/arXiv arXiv 2001
[24]

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, [arXiv:1908.10996]

work page internal anchor Pith review arXiv 2020
[25]

Coccia and C

L. Coccia and C. F. Uhlemann,Mapping out the internal space in AdS/BCFT with Wilson loops, JHEP03(2022) 127, [arXiv:2112.14648]

work page arXiv 2022
[26]

C. F. Uhlemann,Islands and Page curves in 4d from Type IIB, JHEP08(2021) 104, [arXiv:2105.00008]

work page arXiv 2021
[27]

Karch, H

A. Karch, H. Sun, and C. F. Uhlemann,Double holography in string theory, JHEP10 (2022) 012, [arXiv:2206.11292]

work page arXiv 2022
[28]

He and C

D. He and C. F. Uhlemann,SolvingN= 4 SYM BCFT matrix models at large N, JHEP12 (2024) 164, [arXiv:2409.13016]

work page arXiv 2024
[29]

H. Z. Chen, R. C. Myers, D. Neuenfeld, I. A. Reyes, and J. Sandor,Quantum Extremal Islands Made Easy, Part I: Entanglement on the Brane, JHEP10(2020) 166, [arXiv:2006.04851]

work page arXiv 2020
[30]

H. Z. Chen, R. C. Myers, D. Neuenfeld, I. A. Reyes, and J. Sandor,Quantum Extremal Islands Made Easy, Part II: Black Holes on the Brane, JHEP12(2020) 025, [arXiv:2010.00018]

work page arXiv 2020
[31]

Emparan, A

R. Emparan, A. M. Frassino, M. Sasieta, and M. Tomaˇ sevi´ c,Holographic complexity of quantum black holes, JHEP02(2022) 204, [arXiv:2112.04860]

work page arXiv 2022
[32]

A. M. Frassino, J. F. Pedraza, A. Svesko, and M. R. Visser,Higher-Dimensional Origin of Extended Black Hole Thermodynamics, Phys. Rev. Lett.130(2023), no. 16 161501, [arXiv:2212.14055]

work page arXiv 2023
[33]

Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime

N. Engelhardt and A. C. Wall,Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime, JHEP01(2015) 073, [arXiv:1408.3203]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[34]

Emparan, A

R. Emparan, A. M. Frassino, and B. Way,Quantum BTZ black hole, JHEP11(2020) 137, [arXiv:2007.15999]

work page arXiv 2020
[35]

Israel,Singular hypersurfaces and thin shells in general relativity, Nuovo Cim

W. Israel,Singular hypersurfaces and thin shells in general relativity, Nuovo Cim. B44S10 (1966) 1. [Erratum: Nuovo Cim.B 48, 463 (1967)]

work page 1966
[36]

S. W. Hawking and D. N. Page,Thermodynamics of Black Holes in anti-De Sitter Space, Commun. Math. Phys.87(1983) 577

work page 1983
[37]

Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space

J. Maldacena, D. Stanford, and Z. Yang,Conformal symmetry and its breaking in two – 19 – dimensional Nearly Anti-de-Sitter space, PTEP2016(2016), no. 12 12C104, [arXiv:1606.01857]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[38]

A Large Mass Hierarchy from a Small Extra Dimension

L. Randall and R. Sundrum,A Large mass hierarchy from a small extra dimension, Phys. Rev. Lett.83(1999) 3370–3373, [hep-ph/9905221]

work page internal anchor Pith review Pith/arXiv arXiv 1999
[39]

Hayward,Gravitational action for space-times with nonsmooth boundaries, Phys

G. Hayward,Gravitational action for space-times with nonsmooth boundaries, Phys. Rev. D 47(1993) 3275–3280

work page 1993
[40]

Gravitational action with null boundaries

L. Lehner, R. C. Myers, E. Poisson, and R. D. Sorkin,Gravitational action with null boundaries, Phys. Rev. D94(2016), no. 8 084046, [arXiv:1609.00207]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[41]

Replica wormholes and the black hole interior

G. Penington, S. H. Shenker, D. Stanford, and Z. Yang,Replica wormholes and the black hole interior, JHEP03(2022) 205, [arXiv:1911.11977]. – 20 –

work page internal anchor Pith review arXiv 2022