The Conical Singularity And Quantum Corrections To Entropy Of Black Hole

S.N.Solodukhin

REVIEW

The Conical Singularity And Quantum Corrections To Entropy Of Black Hole

S.N.Solodukhin

High Energy Physics - Theory · Submitted 1 Jul 1994 · 35 references

Pith's verdict: The structural claim — Schwarzschild carries an extra mass-independent log divergence that Rindler does not — is the real contribution, but the printed algebra from B4 to the 1/45 coefficient does not close.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on October 29, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 3 major objections · 7 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-th/9407001 (version 1)

Pith IDUMFJZTUX, Pith's permanent record of this paper and its review

CitationS.N.Solodukhin. "The Conical Singularity And Quantum Corrections To Entropy Of Black Hole." arXiv:hep-th/9407001 (1994). https://pith.science/paper/UMFJZTUX

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

The thing to take from this paper is structural, not numerical: the cross term between the regular Riemann tensor at the horizon and the conical part of the curvature produces a log divergence for Schwarzschild that Rindler space simply does not have, and it survives M→∞ because A_h ∝ M² cancels the 1/β_H² from R^reg_{φρφρ}(0) = 4/β_H². That is a statement about topology, not just near-horizon geometry, and it is why the paper gets cited. The smoothed-cone device itself — R_con = 2(α−1)α δ(ρ) from the regularized surface — is clean, reusable, and the 2D Rindler entropy landing on Callan–Wilczek is a real external check rather than a self-consistency exercise. The 2D dilaton black hole correction in Eqs. (66)–(67) is new, and the observation that the temperature is no longer T_H once that term is included is honest about what backreaction will do to it. The paper also says plainly that the classical solution is not the extremum of the one-loop effective action, which is the right thing to say and rarely said in 1994 papers of this kind. Now the soft spot, and it is on the headline number. Eq. (84) gives the B4 coefficient as 32π²/70; running that through G_inf = −(1/32π²)B4 log(Lμ) yields A_h/(1120M²)·log, while Eq. (86) prints A_h/(720πM²)·log — a factor of about two apart. Eq. (85) also writes A_h M² where dimensions demand A_h/M². The 1/45 in Eq. (87) does follow from Eq. (86) with A_h = 16πM², so the quoted number is internally consistent with (86) but not reproducible from (84). Since 1/45 is what people quote, that gap should be closed. On the reader's worry about ε = L^{−1}: I think it is less load-bearing than it looks. The extra log divergence comes from B4 log(Lμ), and its coefficient is independent of the identification; only the argument of the log and the reading of the 1/ε² piece depend on it. The paper argues the identification physically and matches to ζ-function, which is the right kind of argument, just not a derivation. Minor: ref. [12], the cone regularization itself, is unpublished, and the claim that extra divergences from the finite part scale as (α−1)² rests on preprint [29]. Normal for the period, but the load-bearing pieces are external. Verdict: send it out. A referee should force the B4 arithmetic to be redone and printed. Anyone working on horizon entanglement entropy should read it; the structural statement is what travels.

Referee report

Significance

If the central claims hold, the paper makes a useful structural point: the entropy of a black hole is not simply the flat-space geometric entropy scaled by horizon area, because the cross term between the regular Riemann tensor at the horizon and the conical Riemann tensor produces a logarithmic divergence that is mass-independent and survives M to infinity. The two-dimensional analysis is a genuine external check, since Eq. (29) reproduces the published Callan-Wilczek result, and the identification of the L-squared divergence with renormalization of the gravitational coupling (Eq. (79)) anticipates what became a standard viewpoint. The paper is explicit about its own uncertainty at Eq. (65), where it states the result is worth checking by an alternative calculation; that candor is a strength of presentation but also flags that the algebra has not been independently cross-checked.

Major objections (3)

[Eqs. (84)-(87)] The headline coefficient 1/45 in Eq. (87) cannot be reproduced from the printed steps, and this is load-bearing for the paper's central quantitative claim. Eq. (85) writes the cross-term contribution as (alpha-1)(alpha^2+alpha+1)/(2160 pi alpha^2) times A_h M^2 times log(L mu), but A_h M^2 has dimensions of length to the fourth while G_eff must be dimensionless; the combination should be A_h/M^2, as Eq. (86) indeed uses. Even granting that as a typographical slip, the coefficient in Eq. (84), 32 pi^2/70, gives S_q = (3/70)(A_h/beta_H^2) log, whereas Eq. (86) gives A_h/(720 pi M^2) log, a discrepancy of roughly a factor of six. The manuscript shows no intermediate algebra by which a reader could decide which expression is correct, and Eq. (87) inherits the ambiguity. Since the 1/45 term is the paper's principal four-dimensional result, the derivation of Eqs. (84)-(87) needs to be shown step by step, or the coefficient corrected.
[Paragraph following Eq. (27)] The identification of the cone-tip regulator epsilon with the inverse ultraviolet cutoff L^{-1} is asserted on physical grounds and justified only by matching Eq. (28) to the zeta-function result of Callan and Wilczek. This identification sets the units for every divergent coefficient quoted later, including the 1/45 term in Eq. (87) and the L^2 coefficient in Eq. (78). The paper should state explicitly which results depend on this identification and which do not; in particular, whether the structural claim that the Schwarzschild logarithmic divergence survives M to infinity is independent of it. As written, a reader cannot separate the robust structural statement from the convention-dependent coefficient.
[Eqs. (72)-(76) and (84)-(85)] The treatment of the additional (alpha-1)^2/a^2 divergence arising from the finite, non-local part of the effective action rests on the assertion that it does not contribute to the entropy because it is proportional to (alpha-1)^2. This is plausible given the entropy formula (11), but the argument is made by analogy with the two-dimensional case and by appeal to Refs. [29] rather than demonstrated in four dimensions. Since the paper's renormalization claim in the abstract (s7) depends on knowing which divergences do and do not reach the entropy, this point deserves an explicit demonstration or a clearly flagged assumption.

Minor objections (7)

[Eq. (17) and Eq. (70)] The distributional curvature of the cone is stated without derivation; a short appendix showing the limit a to 0 of the smoothed-surface calculation would make the central geometric input self-contained.
[Eq. (25) and Eq. (26)] The harmonic function w and its value w(0) at the cone tip appear in the finite part of the effective action, and the entropy result (29) is obtained by setting w(0) = 0. The justification for this choice, and its effect on the entropy, should be stated.
[Eq. (44) and Eq. (46)] The constant b = 2/beta is fixed by matching to the cone solution near rho = 0, and the resulting energy density (46) is then interpreted as a thermal state. A sentence connecting this choice of quantum state to the standard Unruh/Hartle-Hawking vacua would help the reader place the result.
[Eq. (65)] The paper states that the infinite part of the effective action is worth checking by an alternative calculation, for example with the zeta function. Given that this is the quantity from which the entropy correction (66) follows, performing or at least outlining that check would strengthen the two-dimensional result considerably.
[Eq. (67)] The total entropy is written in terms of the classical mass M and Hawking temperature beta_H, but the paper then notes that the temperature defined as the inverse of partial_M S is no longer T_H. It would be useful to state explicitly the corrected temperature to leading order, so the reader can see the size of the backreaction effect the paper is pointing to.
[References] Several key comparisons rest on preprints (Refs. [29], [32], [33]) that were unpublished at the time of writing; the text should make clear which comparisons are to published results and which are to preprints, so the reader can weigh them accordingly.
[General] The manuscript contains a number of typographical and notational inconsistencies, including the metric ansatz in Eq. (69) where the coefficient of d phi^2 appears to be missing a rho^2 factor, and the use of beta both for the inverse temperature and for the metric function in Eq. (32). A careful pass over the equations would improve readability.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

The paper argues that smoothing the Euclidean cone reveals an extra logarithmic divergence in Schwarzschild black-hole entropy that survives the infinite-mass limit.

The reading

The paper asks how one-loop matter fluctuations change the Bekenstein-Hawking entropy when the Euclidean gravitational saddle is not at the Hawking temperature and therefore has a conical singularity at the horizon. Its strategy is to replace the sharp cone by a smooth surface, read off the curvature, and then use the known one-loop effective action on regular manifolds to compute the entropy through the Gibbons-Hawking partition function. In two dimensions it recovers the logarithmic Rindler divergence, finds a finite mass-dependent correction for the eternal black hole, and in four dimensions finds the expected quadratic Rindler divergence plus an extra logarithmic term for Schwarzschild that does not vanish as the mass goes to infinity. The paper argues that these infinities are absorbed by renormalizing the gravitational coupling, so the correction is tied to the coupling that defines the entropy rather than being a disposable artifact of the regulator.

What carries the argument

The load-bearing device is the replacement of the conical metric $ds^2=dρ^2+α^2ρ^2dφ^2$ by a smooth surface embedded in three dimensions, with metric $ds^2=(ρ^2+a^2α^2)/(ρ^2+a^2)dρ^2+α^2ρ^2dφ^2$, and then taking $a→0$. This gives a controlled curvature $R_{con}=2(α-1)αδ(ρ)$, so ordinary determinant and heat-kernel results can be applied. The same device is used to split the four-dimensional Riemann tensor into a conical part plus a regular part, which is what lets the author isolate the extra Schwarzschild term from the regular curvature at the horizon.

Extended reading notes

Core claim

The central claim is that the one-loop quantum correction to a four-dimensional Schwarzschild black hole's entropy is not just the flat Rindler result scaled by horizon area. Using the smoothed-cone regularization, the paper finds a correction of the form $S_q = A_h/(48πϵ^2)$ plus a logarithmic term in $Σ/ϵ$ for a scalar field, where $A_h$ is the horizon area and $ϵ$ is the short-distance regulator. The first term is the quadratic area-law divergence already seen for Rindler space; the logarithmic term survives the infinite-mass limit and is therefore tied to the black hole's topology and to the regular curvature at the horizon rather than to horizon area alone. In two dimensions the same method gives the logarithmic Rindler divergence and a finite, mass-dependent correction for the eternal black hole. The paper's broader claim is that the $L^2$ divergence is removed by renormalizing the gravitational constant, $κ^{-1}=κ_B^{-1}+L^2$, and the logarithmic divergence by a curvature-squared coupling, so the entropy's infinities track the renormalization of gravitational couplings.

Load-bearing premise

The load-bearing premise is that the distance $ϵ$ from the cone tip can be identified with the inverse ultraviolet cutoff $L^{-1}$, so that one short-distance scale does both jobs; the paper calls this natural and checks it against a zeta-function calculation, but every divergent coefficient and the renormalization argument are stated in units set by that identification.

Editorial extensions

If this is right

The leading Rindler divergence is reproduced in both dimensions: logarithmic in 2D and quadratic in 4D, supporting the use of flat Rindler space for the dominant horizon contribution.
The eternal 2D black hole acquires a finite, mass-dependent entropy correction, so its thermodynamic temperature defined by $∂_M S$ is shifted from the Hawking temperature.
For 4D Schwarzschild, the entropy has a logarithmic term that survives $M→∞$, so the infinite-mass limit does not reduce the full entropy to the Rindler result.
The $L^2$ divergence of the entropy is absorbed by $κ^{-1}=κ_B^{-1}+L^2$, and the logarithmic divergence by a curvature-squared coupling, tying entropy renormalization to gravitational coupling renormalization.
Quantum corrections remain proportional to horizon area at leading order but include a subleading term controlled by topology and horizon curvature.

Reading between the lines

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

If the extra logarithmic term is regulator-independent, horizon area alone cannot fix black-hole entropy even asymptotically; a subleading topological or curvature piece would have to be reproduced by any state-counting derivation.
Because the term is mass-independent while the area term scales as $M^2$, it would dominate the entropy of sufficiently small black holes; if the one-loop treatment survives there, late-stage evaporation thermodynamics would be modified.
The smoothed-cone picture suggests a concrete numerical check: vary the core radius $a$ of the regularized cone and see whether the entropy coefficient is stable before taking $a→0$.
The renormalization pattern hints that a microscopic theory should predict the finite constant left after the gravitational couplings are renormalized, since the divergent part alone does not fix the entropy.

Original abstract

For general finite temperature different from the Hawking one there appears a well known conical singularity in the Euclidean classical solution of gravitational equations. The method of regularizing the cone by regular surface is used to determine the curvature tensors for such a metrics. This allows one to calculate the one-loop matter effective action and the corresponding one-loop quantum corrections to the entropy in the framework of the path integral approach of Gibbons and Hawking. The two-dimensional and four-dimensional cases are considered. The entropy of the Rindler space is shown to be divergent logarithmically in two dimensions and quadratically in four dimensions that coincides with results obtained earlier. For the eternal 2D black hole we observe finite, dependent on the mass, correction to the entropy. The entropy of the 4D Schwarzschild black hole is shown to possess an additional (in comparison with the 4D Rindler space) logarithmically divergent correction which does not vanish in the limit of infinite mass of the black hole. We argue that infinities of the entropy in four dimensions are renormalized by the renormalization of the gravitational coupling.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,269 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.24 · human participants 0.01 · controlled comparison 0.25 · randomized assignment 0.01 · states quantitative result 0.33 · compares with prior results 0.94 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

For general finite temperature different from the Hawking one there appears a well known conical singularity in the Euclidean classical solution of gravitational equations. The method of regularizing the cone by regular surface is used to determine the curvature tensors for such a metrics. This allows one to calculate the one-loop matter effective action and the corresponding one-loop quantum corrections to the entropy in the framework of the path integral approach of Gibbons and Hawking. The two-dimensional and four-dimensional cases are considered. The entropy of the Rindler space is shown to be divergent logarithmically in two dimensions and quadratically in four dimensions that coincides with results obtained earlier. For the eternal 2D black hole we observe finite, dependent on the mass, correction to the entropy. The entropy of the 4D Schwarzschild black hole is shown to possess an additional (in comparison with the 4D Rindler space) logarithmically divergent correction which does not vanish in the limit of infinite mass of the black hole. We argue that infinities of the entropy in four dimensions are renormalized by the renormalization of the gravitational coupling.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	For general finite temperature different from the Hawking one there appears a well known conical singularity in the Euclidean classical solution of gravitational equations.	background 1.00	0.07	0.03	asserted 1.00
s1	The method of regularizing the cone by regular surface is used to determine the curvature tensors for such a metrics.	method 0.99	0.73	0.02	asserted 0.98
s2	This allows one to calculate the one-loop matter effective action and the corresponding one-loop quantum corrections to the entropy in the framework of the path integral approach of Gibbons and Hawking.	method 0.93	0.68	0.09	asserted 0.74
s3	The two-dimensional and four-dimensional cases are considered.	contribution 0.74	0.64	0.02	asserted 0.77
s4	The entropy of the Rindler space is shown to be divergent logarithmically in two dimensions and quadratically in four dimensions that coincides with results obtained earlier.	result 1.00	0.55	0.13	asserted 1.00
s5	For the eternal 2D black hole we observe finite, dependent on the mass, correction to the entropy.	result 1.00	0.89	0.12	asserted 0.99
s6	The entropy of the 4D Schwarzschild black hole is shown to possess an additional (in comparison with the 4D Rindler space) logarithmically divergent correction which does not vanish in the limit of infinite mass of the black hole.	result 1.00	0.88	0.33	asserted 1.00
s7	We argue that infinities of the entropy in four dimensions are renormalized by the renormalization of the gravitational coupling.	interpretation 1.00	0.54	0.50	hedged possibility 0.45

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (35)

[12]

D.V.Fursaev, S.N.Solodukhin, unpublished

View on Pith
[29]

D.V.Fursaev, Spectral geometry and one-loop divergencies on manifolds w ith conical singularities, DSF-13/94; J.S.Dowker, Heat kernels on curved cones , MUTP/94/09

View on Pith
[1]

G. ’t Hooft, Nucl.Phys. B256 (1985), 727

View on Pith 1985
[2]

L.Bombelli, R.Koul, J.Lee and R.Sorkin, Phys.Rev. D34 (1986), 373

View on Pith 1986
[3]

M.Srednicki, Phys.Rev.Lett. 71 (1993), 666

View on Pith 1993
[4]

V.Frolov, I.Novikov, Phys.Rev. D48 (1993), 4545

View on Pith 1993
[5]

C.Callan, F.Wilczek. On geometric entropy , hep-th/9401072

View on Pith Pith review arXiv
[6]

D.Kabat, M.J.Strassler, A comment on entropy and area , hep-th/9401125

View on Pith Pith review arXiv
[7]

C.Holzhey, F.Larsen, F.Wilczek, Geometric and renormalized entropy in conformal theory, hep-th/9403108

View on Pith Pith review arXiv
[8]

J.S.Dowker, Remarks on geometric entropy , hep-th/9401159. 21

View on Pith Pith review arXiv
[9]

G.W.Gibbons, S.W.Hawking, Phys.Rev. D15 (1977), 2752; S.W.Hawking in General Relativity, edited by S.W.Hawking and W.Israel (Cambridge University Press, Cam- bridge, 1979)

View on Pith 1977
[10]

S.Carlip, C.Teitelboim, The oﬀ-shell black hole , gr-qc/9312002; C.Teitelboim, Topo- logical roots of black hole entropy , preprint, April 1994

View on Pith Pith review arXiv 1994
[11]

K.Schleich, D.M.Witt, Nucl.Phys. B402 (1993), 411; 469

View on Pith 1993
[13]

D.D.Sokolov, A.A.Starobinsky, DAN SSSR, 22 (1977), 312

View on Pith 1977
[14]

E.S.Fradkin, A.A.Tseytlin, Ann.Phys. 143 (1982), 413

View on Pith 1982
[15]

H.P.McKean, I.M.Singer, J.Diﬀ.Geometry, 1 (1967), 43; J.Cheeger, J.Diﬀ.Geometry, 18 (1983), 575

View on Pith 1967
[16]

L.D.Landau, E.M.Lifshits, Statistical Physics, Nauka, Moscow 1964

View on Pith 1964
[17]

R.B.Mann, A.Shiekh and L.Tarasov, Nucl.Phys. B341 (1990), 134

View on Pith 1990
[18]

S.M.Christensen, S.A.Fulling, Phys.Rev. D15 (1977), 2088

View on Pith 1977
[19]

G.Mandal, A.Sengupta and S.Wadia, Mod.Phys.Lett. A6 (1991), 1685; E.Witten, Phys.Rev. D44 (1991), 314

View on Pith 1991
[20]

C.Nappi, A.Pasquinucci, Mod.Phys.Lett. A17 (1992), 3337

View on Pith 1992
[21]

G.W.Gibbons and M.Perry, Int.J.Mod.Phys. D1 (1992), 335; V.P.Frolov, Phys.Rev. D46 (1992), 5383

View on Pith 1992
[22]

J.G.Russo, L.Susskind, L.Thorlacius, Phys.Rev. D46 (1992), 3444

View on Pith 1992
[23]

R.B.Mann, Liouville black holes , hep-th/9308034

View on Pith Pith review arXiv
[24]

S.N.Solodukhin, On higher derivative gravity in two dimensions , JINR preprint, E2- 94-185. 22

View on Pith
[25]

E.Keski-Vakkuri, S.D.Mathur, Evaporating black holes and entropy , hep-th/9312194

View on Pith Pith review arXiv
[26]

T.M.Fiola, J.Preskill, A.Strominger, S.P.Trivedi, Black hole thermodynamics and information loss in two dimensions , hep-th/9403137

View on Pith Pith review arXiv
[27]

R.C.Myers, Black hole entropy in two dimensions , hep-th/9405162

View on Pith Pith review arXiv
[28]

B.S.De Witt, Phys.Repts. C19 (1975), 295

View on Pith 1975
[30]

N.D.Birrell, P.C.W.Devies, Quantum ﬁelds in curved space , Cambridge University Press, Cambridge, 1982

View on Pith 1982
[31]

D.V.Fursaev, Class.Quant.Grav. 11 (1994), 1431

View on Pith 1994
[32]

L.Susskind, J.Uglum, Black hole entropy in canonical quantum gravity and superst ing theory, SU-ITP-94-1, hep-th/9401076

View on Pith Pith review arXiv
[33]

A.O.Barvinsky, V.P.Frolov and A.I.Zelnikov, Wavefunction of a black hole and the dynamical origin of entropy , preprint, April 1994

View on Pith 1994
[34]

L.Susskind, Some speculations about black hole entropy in string theory , RU-93-44, hep-th/9309145

View on Pith Pith review arXiv
[35]

E.S.Fradkin, A.A.Tseytlin, Nucl.Phys. B261 (1985), 1. 23

View on Pith 1985

Forward citations

Cited by 34 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

A Quantum Focussing Conjecture
hep-th 2015-06 conditional novelty 8.0 of 10

A single conjectured inequality on generalized entropy is shown to imply the Bousso bound, the generalized second law, and a new Quantum Null Energy Condition on stress-energy.
Black hole free energy landscapes from constrained instantons
gr-qc 2026-10 conditional novelty 7.0 of 10

A path integral derivation shows that the generalized black hole free energy landscape F_gen = E_B - Omega_B J_B - T S arises from constrained instantons with partial-Neumann boundary conditions, extending to higher-c...
Proof of the Quantum Null Energy Condition
hep-th 2015-09 conditional novelty 7.0 of 10

The Quantum Null Energy Condition, a conjectured lower bound on the stress tensor in terms of the second variation of entropy, is proven for free and superrenormalizable bosonic fields on stationary null surfaces.
Quantum corrections to holographic entanglement entropy
hep-th 2013-07 accept novelty 7.0 of 10

The one-loop correction to holographic entanglement entropy is the bulk entanglement entropy between the region behind the Ryu-Takayanagi surface and its complement, plus local Wald-like and counterterm contributions.
Entanglement entropy for the n-sphere
hep-th 2010-07 accept novelty 7.0 of 10

The logarithmic coefficient of the entanglement entropy for a sphere and a conformal scalar is computed exactly in any dimension: -1/3 in 2D, 1/90 in 4D, and zero in odd spacetime dimensions.

Show 29 more citing papers

Logarithmic corrections to the entropy of near-extremal rotating black holes
hep-th 2026-09 conditional novelty 6.0 of 10

For near-extremal rotating BMPV black holes the log T entropy correction is (3/2)log(T/T_Sch) + (1/2)log(T/T_Rot) + (3/2)log(T/T_SU(2)), obtained from explicitly constructed Schwarzian, rotational, and SU(2) zero modes.
Polyakov-loop potential of accelerated gluonic matter and thermodynamic subtleties
hep-ph 2026-05 unverdicted novelty 6.0 of 10

Real acceleration strengthens deconfining properties of gluonic matter per the one-loop Polyakov-loop potential minimized in the optical metric, while imaginary acceleration yields a confined phase.
Quiver superconformal index and giant gravitons: asymptotics and expansions
hep-th 2025-09 conditional novelty 6.0 of 10

For toric quiver theories, coefficients of the large-N superconformal index grow like exp(constant*sqrt(n)) times n^((m-5)/4) for the A-hat_m family, with polynomial growth for dP3 and Y^{p,0}.
Echo of the Dark: gravitational waves from dark SU(3) Yang-Mills theory
hep-ph 2022-10 conditional novelty 6.0 of 10

In a holographic model matched to lattice Yang-Mills thermodynamics, the confinement transition of a dark SU(3) gauge sector produces gravitational waves too faint for next-generation detectors.
Higher derivative corrections to Kerr black hole thermodynamics
hep-th 2019-01 accept novelty 6.0 of 10

Evaluating six- and eight-derivative curvature terms on the unperturbed Kerr metric yields closed-form corrections to its thermodynamic quantities, with the eight-derivative entropy shift provably non-negative for pos...
Proof of the Weak Gravity Conjecture from Black Hole Entropy
hep-th 2018-01 conditional novelty 6.0 of 10

Positivity of higher-derivative corrections to black hole entropy implies that extremal black holes are unstable to decay, which satisfies the weak gravity conjecture within theories whose ultraviolet completion is tr...
Universal Entanglement and Boundary Geometry in Conformal Field Theory
hep-th 2015-09 conditional novelty 6.0 of 10

The universal logarithmic entanglement entropy across a sphere in even-dimensional CFT equals a boundary contribution from the dimensionally continued Euler characteristic, giving S_E = (-1)^{d/2} 4a ln(delta/ell).
On the Architecture of Spacetime Geometry
hep-th 2012-12 conditional novelty 6.0 of 10

The Bekenstein-Hawking area law is conjectured to give the leading entanglement entropy of any large region in a smooth spacetime, not only of black hole horizons.
Logarithmic Corrections to Schwarzschild and Other Non-extremal Black Hole Entropy in Different Dimensions
hep-th 2012-05 accept novelty 6.0 of 10

Euclidean one-loop gravity yields a definite logarithmic correction to non-extremal black hole entropy in D dimensions, which for four-dimensional Schwarzschild disagrees with the loop quantum gravity prediction.
Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions
hep-th 2011-09 accept novelty 6.0 of 10

Logarithmic corrections to rotating extremal black hole entropy are computed from Euclidean quantum gravity and match the microscopic string theory index for BMPV black holes.
Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates
hep-th 2011-08 accept novelty 6.0 of 10

Half-BPS black holes in N=2 supergravity carry a logarithmic entropy correction of (1/12)(23 + n_H - n_V) ln(A_H/G_N), fixed entirely by the massless spectrum and computable from the near-horizon geometry.
Logarithmic Corrections to N=4 and N=8 Black Hole Entropy: A One Loop Test of Quantum Gravity
hep-th 2011-06 accept novelty 6.0 of 10

One-loop gravitational corrections to N=4 and N=8 extremal black hole entropy reproduce the microscopic index results, vanishing for N=4 and giving minus 2 ln Delta for N=8.
Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
hep-th 2010-05 accept novelty 6.0 of 10

The one-loop contribution of all matter multiplet fields to the logarithmic correction of quarter BPS black hole entropy cancels to zero, making the correction independent of the number of matter multiplets.
Aspects of Holographic Entanglement Entropy
hep-th 2006-05 conditional novelty 6.0 of 10

Entanglement entropy in a conformal field theory equals the area of a minimal surface in its dual anti-de Sitter space, divided by four times Newton's constant.
Black Hole Entropy and Entropy of Entanglement
hep-th 1995-03 conditional novelty 6.0 of 10

For scalar and spin-half fields the one-loop black hole entropy equals the entanglement entropy, but for an Abelian gauge field the two differ by a horizon-localized contact term with no thermal or state-counting inte...
Black Hole Entropy and Holographic Entanglement Entropy in DGP Brane Gravity
hep-th 2026-10 conditional novelty 5.0 of 10

In DGP braneworlds, black hole entropy equals holographic entanglement entropy precisely when the brane extrinsic curvature satisfies a condition that is automatic for static black holes, and the same condition govern...
Entanglement Entropy and Thermodynamics of Dynamical Black Holes
hep-th 2025-09 unverdicted novelty 5.0 of 10

In f(R) theories, the replica-method gravitational entropy computed on the apparent horizon matches the Hollands-Wald-Zhang dynamical black hole entropy and satisfies the first law, while the event horizon does not; t...
On the late time behavior of thermal two point function in curved space-time
hep-th 2025-09 conditional novelty 5.0 of 10

For thermal Bose fields in static de Sitter or a planar BTZ black hole, the late-time correlation decay switches from temperature-limited to quasinormal-mode-limited at a critical temperature Tc.
Quantum-corrected black hole thermodynamics from the gravitational path integral
hep-th 2025-06 conditional novelty 5.0 of 10

Including off-shell geometries at one-loop order in the ensemble-averaged path integral yields logarithmic entropy corrections and a phase diagram with zero-order phase transitions for RN-AdS black holes.
Soft hairy horizons in three spacetime dimensions
hep-th 2016-11 conditional novelty 5.0 of 10

In three-dimensional flat space, horizons carry the same infinite Heisenberg near-horizon symmetry algebra as in anti-de Sitter space, and the resulting entropy matches a KdV-hierarchy counting formula.
Entanglement Entropy: A Perturbative Calculation
hep-th 2014-03 conditional novelty 5.0 of 10

A Euclidean path-integral framework computes first-order corrections to entanglement entropy for slightly deformed planar and spherical surfaces in four-dimensional CFTs, matching Solodukhin's universal logarithmic term.
Renormalization of Entanglement Entropy and the Gravitational Effective Action
hep-th 2013-02 accept novelty 5.0 of 10

For path-integral states with a boost symmetry about the entangling surface, the UV divergences of entanglement entropy match those of the gravitational effective action, leaving a finite Bekenstein-Hawking area term.
Holographic Entanglement Entropy in Lovelock Gravities
hep-th 2011-01 conditional novelty 5.0 of 10

The generalized Wald-entropy formula for holographic entanglement entropy in Lovelock gravity reproduces the conformal-anomaly coefficients of the dual CFT for balls and cylinders, including a nontrivial cubic-Lovelock check.
Entanglement entropy in free quantum field theory
hep-th 2009-05 accept novelty 3.0 of 10

Free-field entanglement entropy can be reduced to replica partition functions or Gaussian correlators, yielding exact universal results in one, two, and higher dimensions.
Effect of Non-Extensive Parameter on Page Curve
hep-th 2025-02 reject novelty 2.0 of 10

The entanglement entropy of Hawking radiation in non-extensive entropy-corrected Schwarzschild black holes grows linearly until an island forms and later saturates, with the Page time depending on the entropy deformat...
Microscopic and Macroscopic Entropy of Extremal Black Holes in String Theory
hep-th 2014-02 accept novelty 2.0 of 10

String theory's microstate counts match the entropy of extremal supersymmetric black holes, including logarithmic and finite quantum corrections, in every case where both sides can be computed.
Entanglement Entropy from a Holographic Viewpoint
gr-qc 2012-04 conditional novelty 2.0 of 10

A survey of the Ryu-Takayanagi proposal that entanglement entropy in a conformal field theory equals the area of a minimal surface in its dual anti-de Sitter gravity, with applications to black holes and boundary CFT.
Entanglement entropy of black holes
hep-th 2011-04 accept novelty 2.0 of 10

A systematic review showing that the conical-singularity method computes black hole entanglement entropy whose UV divergences renormalize Newton's constant and quadratic curvature couplings, while non-minimally couple...
Holographic Entanglement Entropy: An Overview
hep-th 2009-05 conditional novelty 1.0 of 10

A 2009 review argues that entanglement entropy in a conformal field theory is computed by the area of a minimal surface in its dual anti-de Sitter spacetime, and surveys the evidence and applications.

How later papers used it

81 later papers cite it

Evidence: substantial. 75 of the citing papers share no author with it, and 12 of those carry a confident label from Pith's citation classifier.

Pith read 11 of the 114 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

2 later papers by other authors are listed below: 2 used its method or tool.

Uses its method or tool 2 of 9 papers with this label

In the latter case, a conical singularity is present at the horizon, and its contribution to the free energy is obtained after regularizing it with a spherical cap (more details are provided in the appendix) [ref] .

Echo of the Dark: gravitational waves from dark SU(3) Yang-Mills theory (2022) · Effective Action from Holography · 0.96
Used this paper's regularized metric to handle the conical singularity along the line r=0.

Entanglement Entropy & Anomaly Inflow (2015) · 0.98 · paraphrased: the licence does not allow quoting

How the literature uses it

79 arXiv papers cite this in 112 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 71 sentences without a confident label

Uses its method or tool 9 papers

The near-horizon geometry, suppressing angular directions, is given by [equation] As proposed in [ref] , in taking $β$-derivatives of the action, one has to consider this family and at the end of the calculation set the periodicity to the Hawking periodicity.

Black Hole Entropy Sourced by String Winding Condensate · Conical singularity · 0.97
This approach was used to study the quantum corrections to the black hole entropy, which is called the off-shell method [ref] .

Generalized free energy landscape of black hole phase transition · Introduction · 0.81
We address this issue by adopting a regularization procedure [ref] .

Generalized Free Energy Landscapes from Iyer-Wald Formalism · Generalized Free Energy · 0.99

Uses its data or values 1 paper

In this case $r_-=0$ ($q=0$) and $r_+=2m$ so that the entropy, found by Solodukhin [ref] , is S_Sch=A(Σ)ø48πϵ^2+1ø45lnr_+øϵ . entropy-Sch Historically this was the first time when the subleading logarithmic term in entanglement entropy was computed.

Entanglement entropy of black holes · The Reissner-Nordström black hole. · 0.88

Compares with it 2 papers

One can also compare the result with the one-loop contributions to black-hole entropy obtained in [ref] by considering conical singularities associated to time coordinate.

Logarithmic Corrections, Entanglement Entropy, and UV Cutoffs in de Sitter Spacetime · $q$-dependent bulk cut-offs · 1.00
Taking the“Brick wall” model [ref] and the “quantum entropy” model [ref] as examples, the logarithmic correction captures the quantum correction from the one-loop effect of matter on a fixed background.

Quantum-corrected black hole thermodynamics from the gravitational path integral · Quantum corrected black hole thermodynamics · 0.93

Cites it as support 1 paper

There is compelling evidence that this divergence is cancelled by a renormalization of Newton's constant in the area term [ref] .

Generalized Second Law for Cosmology · Generalized Entropy and Quantum Expansion · 0.96

Cites it as background 26 papers

In this case the dominant contribution to the entropy comes from the Bekenstein-Hawking term, but it can receive subleading corrections proportional to the logarithm of the horizon area [ref] .

Logarithmic Corrections to Schwarzschild and Other Non-extremal Black Hole Entropy in Different Dimensions · Introduction · 0.80
Both the area law of entropy and its logarithmic corrections are universal features of gravitational theories [ref] .

Logarithmic corrections to entropy of 3D cosmological solutions from celestial dual · Introduction · 0.96
The calculation of the entanglement entropy of a static black hole is discussed in the following papers [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] .

Entanglement entropy of black holes · The dilatonic charged black hole · 0.98

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [12]

D.V.Fursaev, S.N.Solodukhin, unpublished

View on Pith

[2] [29]

D.V.Fursaev, Spectral geometry and one-loop divergencies on manifolds w ith conical singularities, DSF-13/94; J.S.Dowker, Heat kernels on curved cones , MUTP/94/09

View on Pith

[3] [1]

G. ’t Hooft, Nucl.Phys. B256 (1985), 727

View on Pith 1985

[4] [2]

L.Bombelli, R.Koul, J.Lee and R.Sorkin, Phys.Rev. D34 (1986), 373

View on Pith 1986

[5] [3]

M.Srednicki, Phys.Rev.Lett. 71 (1993), 666

View on Pith 1993

[6] [4]

V.Frolov, I.Novikov, Phys.Rev. D48 (1993), 4545

View on Pith 1993

[7] [5]

C.Callan, F.Wilczek. On geometric entropy , hep-th/9401072

View on Pith Pith review arXiv

[8] [6]

D.Kabat, M.J.Strassler, A comment on entropy and area , hep-th/9401125

View on Pith Pith review arXiv

[9] [7]

C.Holzhey, F.Larsen, F.Wilczek, Geometric and renormalized entropy in conformal theory, hep-th/9403108

View on Pith Pith review arXiv

[10] [8]

J.S.Dowker, Remarks on geometric entropy , hep-th/9401159. 21

View on Pith Pith review arXiv

[11] [9]

G.W.Gibbons, S.W.Hawking, Phys.Rev. D15 (1977), 2752; S.W.Hawking in General Relativity, edited by S.W.Hawking and W.Israel (Cambridge University Press, Cam- bridge, 1979)

View on Pith 1977

[12] [10]

S.Carlip, C.Teitelboim, The oﬀ-shell black hole , gr-qc/9312002; C.Teitelboim, Topo- logical roots of black hole entropy , preprint, April 1994

View on Pith Pith review arXiv 1994

[13] [11]

K.Schleich, D.M.Witt, Nucl.Phys. B402 (1993), 411; 469

View on Pith 1993

[14] [13]

D.D.Sokolov, A.A.Starobinsky, DAN SSSR, 22 (1977), 312

View on Pith 1977

[15] [14]

E.S.Fradkin, A.A.Tseytlin, Ann.Phys. 143 (1982), 413

View on Pith 1982

[16] [15]

H.P.McKean, I.M.Singer, J.Diﬀ.Geometry, 1 (1967), 43; J.Cheeger, J.Diﬀ.Geometry, 18 (1983), 575

View on Pith 1967

[17] [16]

L.D.Landau, E.M.Lifshits, Statistical Physics, Nauka, Moscow 1964

View on Pith 1964

[18] [17]

R.B.Mann, A.Shiekh and L.Tarasov, Nucl.Phys. B341 (1990), 134

View on Pith 1990

[19] [18]

S.M.Christensen, S.A.Fulling, Phys.Rev. D15 (1977), 2088

View on Pith 1977

[20] [19]

G.Mandal, A.Sengupta and S.Wadia, Mod.Phys.Lett. A6 (1991), 1685; E.Witten, Phys.Rev. D44 (1991), 314

View on Pith 1991

[21] [20]

C.Nappi, A.Pasquinucci, Mod.Phys.Lett. A17 (1992), 3337

View on Pith 1992

[22] [21]

G.W.Gibbons and M.Perry, Int.J.Mod.Phys. D1 (1992), 335; V.P.Frolov, Phys.Rev. D46 (1992), 5383

View on Pith 1992

[23] [22]

J.G.Russo, L.Susskind, L.Thorlacius, Phys.Rev. D46 (1992), 3444

View on Pith 1992

[24] [23]

R.B.Mann, Liouville black holes , hep-th/9308034

View on Pith Pith review arXiv

[25] [24]

S.N.Solodukhin, On higher derivative gravity in two dimensions , JINR preprint, E2- 94-185. 22

View on Pith

[26] [25]

E.Keski-Vakkuri, S.D.Mathur, Evaporating black holes and entropy , hep-th/9312194

View on Pith Pith review arXiv

[27] [26]

T.M.Fiola, J.Preskill, A.Strominger, S.P.Trivedi, Black hole thermodynamics and information loss in two dimensions , hep-th/9403137

View on Pith Pith review arXiv

[28] [27]

R.C.Myers, Black hole entropy in two dimensions , hep-th/9405162

View on Pith Pith review arXiv

[29] [28]

B.S.De Witt, Phys.Repts. C19 (1975), 295

View on Pith 1975

[30] [30]

N.D.Birrell, P.C.W.Devies, Quantum ﬁelds in curved space , Cambridge University Press, Cambridge, 1982

View on Pith 1982

[31] [31]

D.V.Fursaev, Class.Quant.Grav. 11 (1994), 1431

View on Pith 1994

[32] [32]

L.Susskind, J.Uglum, Black hole entropy in canonical quantum gravity and superst ing theory, SU-ITP-94-1, hep-th/9401076

View on Pith Pith review arXiv

[33] [33]

A.O.Barvinsky, V.P.Frolov and A.I.Zelnikov, Wavefunction of a black hole and the dynamical origin of entropy , preprint, April 1994

View on Pith 1994

[34] [34]

L.Susskind, Some speculations about black hole entropy in string theory , RU-93-44, hep-th/9309145

View on Pith Pith review arXiv

[35] [35]

E.S.Fradkin, A.A.Tseytlin, Nucl.Phys. B261 (1985), 1. 23

View on Pith 1985