Evanescent Black Holes

A. Strominger; C. Callan; J. Harvey; S. Giddings

REVIEW

Evanescent Black Holes

C. Callan, S. Giddings, J. Harvey, A. Strominger

High Energy Physics - Theory · Submitted 28 Nov 1991 · 11 references

Pith's verdict: The CGHS model is the durable contribution — an exactly solvable 2D dilaton gravity with a clean one-loop Hawking flux — while the evanescent-black-hole conclusion is a flagged conjecture whose key step, the pulse crossing a timelike dilaton–Liouville boundary, is asserted rather than shown.

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arXiv IDhep-th/9111056 (version 1)

Pith IDCJVDDQ63, Pith's permanent record of this paper and its review

CitationA. Strominger, C. Callan, J. Harvey, S. Giddings. "Evanescent Black Holes." arXiv:hep-th/9111056 (1991). https://pith.science/paper/CJVDDQ63

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Editor's note

read the letter

Worth your time, but read it for the model, not the conclusion. The compiled record says the authors state no limitations; that's wrong — the conclusion paragraph is explicit about what hasn't been shown, and you should read it that way. What's solid: the action (1) is exactly solvable classically, and Eqs. (6)–(11) give the general solution and the black hole in closed form — checkable in an afternoon. The shock-wave solution (13) is clean. The Hawking flux via the trace anomaly (16)–(19) is standard and correctly done, including the mass-independent asymptotic rate. The large-N effective action (23) with the induced Liouville term is the piece that mattered: it turns backreaction into a classical boundary-value problem, and that is what everyone after this paper actually used. Where it's soft: the abstract's claim [abstract:s4] is a conjecture, and the authors say so — 'must at present be regarded as speculative,' large-N equations unsolved, second-order perturbation divergent at the boundary. That's honest and I don't hold it against them. Two steps beyond that admission deserve a flag. First, 'this dividing line is timelike' is read off the classical level set in (13); nothing shows the quantum-corrected level set e^{-2φ} ~ N/12 keeps that causal character, and the energy-conservation inference depends on the pulse crossing it. Second, the decrease of the Bondi mass to zero is asserted ('it is plausible') rather than derived from (23)–(24). The vanishing of M in the Liouville region via (29) is really a gauge statement — no invariant for a flat metric — not a dynamical property of the pulse; the conclusion is right, the reasoning is thinner than the sentence suggests. None of this is misrepresentation. The paper is clear about what it has and hasn't shown, and the model is the durable contribution. Who should read it: anyone working on 2D gravity, holography, or the information paradox — it's a required citation, and a good teaching paper for how to set up a solvable backreaction problem. Peer review: yes, send it out. Even setting aside the historical outcome, the classical and one-loop sectors are checkable and the conjecture is stated with its assumptions visible.

Referee report

Significance

If the picture holds, this is an important paper: it supplies a renormalizable, classically solvable toy model in which the black-hole information problem can be posed sharply, and it makes a structural prediction (no horizon, no singularity, unitary S-matrix on a zero-energy remnant) that is in principle falsifiable by solving the large-N equations. The exact classical solution of Eqs. (6)-(11) and the anomaly computation of Eqs. (16)-(19) are checkable, parameter-free, and have already been used elsewhere. The paper is also to be credited for stating its own limitations plainly rather than overclaiming: it says the picture 'must at present be regarded as speculative,' that the large-N equations have not been solved, and that second-order perturbation theory diverges at the dilaton-Liouville boundary. That candour is a genuine strength and should be preserved in revision.

Major objections (3)

[Global picture, paragraph beginning 'We now have a plausible global picture'] The sentence 'This dividing line is timelike' is load-bearing for the central claim and is asserted rather than derived. The timelike character is read off the classical solution Eq. (13), where e^{-2φ} = M/λ − λ²x⁺x⁻ makes the level set e^{-2φ} = N/12 a hyperbola; nothing in the manuscript establishes that the level set of the quantum-corrected solution retains that causal character. If the corrected level set were spacelike or null somewhere, the incoming pulse need not enter the region where the zero-energy argument of Eq. (29) applies, and the energy-conservation inference ('all of the initial energy of the wavepacket must have radiated away to I^+_R') would not go through. A concrete test is available: integrate the constraint equations (24) for a small-amplitude pulse and check the causal character of the level set e^{-2φ} = N/12 in the resulting solution. At minimum the manuscript should state explicitly the condition under which the crossing is guaranteed.
[Bondi mass discussion, Eqs. (24)-(26)] The step M(σ⁻) → 0 as σ⁻ → +∞ is described as 'plausible' and is not derived. The argument given is that the pulse crosses into the Liouville region, where all asymptotically flat states have zero energy, so by energy conservation the energy must have radiated; but this is precisely the crossing step flagged above, and the manuscript does not show that M(σ⁻) decreases monotonically rather than asymptoting to a nonzero value. The authors concede that they have not shown the large-N equations of motion give a well-defined evolution. A useful addition would be an argument, even at the level of the constraint equations (24), that M(σ⁻) is bounded below by zero and monotonically decreasing for the class of initial data considered, together with a statement of what would have to be true of the solution for the asymptote to be nonzero.
[Liouville zero-energy argument, Eq. (29) and following sentence] The vanishing of the Bondi mass in the Liouville region is argued in one sentence: 'if ρ approaches zero on I^+_R as required by the boundary conditions (25), the derivatives of ρ and consequently M must also vanish.' This is compressed and, as written, does not quite establish the conclusion. In Liouville gauge T₊₋ = 0 gives ρ = ρ₊(σ⁺) + ρ₋(σ⁻), so ∂₋δρ = ρ₋′(σ⁻) is independent of σ⁺ and does not vanish merely because ρ → 0 as σ⁺ → ∞ at fixed σ⁻; what is needed is that ρ → 0 for all σ⁻ on I^+_R, which forces ρ₋ to be constant and hence ∂₋ρ → 0. The argument is correct once the additivity of ρ is used explicitly, but the manuscript should spell this out, since Eq. (29) is the sole support for the 'zero-energy bound state' interpretation.

Minor objections (8)

[Abstract, [abstract:s4]] The abstract's 'black holes thereby disappear from the quantum mechanical spectrum' is stronger than the body's conclusion, which is that 'there is no indication that pure states evolve into mixed states.' The abstract should be calibrated to the body's more careful phrasing.
[Footnote 3] The shift of N by the ghost and gravity measures needed to maintain c = 26 is noted as a subleading-in-1/N effect. Since the location of the dividing line is set by e^{-2φ} ~ N/12, it would help to state explicitly that this O(1) shift does not affect the leading-order structure of the two-region picture.
[Footnote 4] The range of ψ = e^{-φ} is left unspecified, with the remark that 'it is not clear what range should be taken.' Since this bears on whether the Liouville region is genuinely part of the same spacetime, a sentence on the consequences of different choices would strengthen the discussion.
[Eq. (19) and following text] The asymptotic flux λ²/48 is mass-independent, which the authors call 'surprising' and attribute to other studies of two-dimensional gravity. A brief physical remark or a specific citation for this feature would help the reader.
[Eq. (20)] The turn-around time is quoted 'to leading order in the mass' without the intermediate integration. One line of algebra showing how the integrated flux reproduces Eq. (20) would make the estimate checkable.
[Eq. (26) and following sentence] The N-dependent term in the Bondi mass is said to vanish 'due to the boundary conditions (25).' It would be clearer to state which of the conditions in (25) is responsible.
[Figures 1 and 2] In Figure 2 the boundary between the 'Dilaton Region' and the 'Liouville Region' should be drawn explicitly, since the causal character of that boundary is central to the argument. The shading in both figures is difficult to read in the current reproduction.
[Footnote 5] The statement that there is no local notion of an apparent horizon in two dimensions would benefit from a reference or a short qualification, as it is used to support the claim that no horizon forms.

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The paper

The paper claims

In a two-dimensional model of gravity with many matter fields, infalling matter appears to radiate away all of its energy before an event horizon or singularity can form, leaving no black hole in the quantum spectrum.

The reading

Hawking's claim that black holes destroy quantum information is hard to test in four dimensions, so this paper builds a tractable substitute: two-dimensional gravity with a dilaton field and $N$ conformal matter fields, chosen because the classical theory is exactly solvable and contains genuine black hole solutions formed by collapsing matter. The authors first exhibit those classical solutions, then compute the Hawking flux exactly using the trace anomaly, and find the usual runaway: the flux is asymptotically constant, so integrating it over all time would remove more energy than the hole ever had. To fix that they promote the matter loops to a leading-order $1/N$ effective action, which adds a Liouville term to the classical theory, and argue that this term splits spacetime into a dilaton region where classical gravity rules and a Liouville region where every asymptotically flat state has zero energy. If that picture holds, an incoming pulse crosses into the zero-energy region, so its Bondi mass must have been radiated away entirely before any horizon could set in. What survives at late times is a zero-energy remnant that still carries the pulse's conserved global charge, which is why the authors expect a unitary $S$-matrix rather than a pure-to-mixed transition.

What carries the argument

The load-bearing device is the leading-order-in-$1/N$ effective action, in which the $N$ matter fields induce a Liouville term $Npartial_+rho partial_-rho/12$ that competes with the classical dilaton term $e^{-2varphi}$. The ratio of these two terms defines a timelike dividing line: where $e^{-2varphi} gg N/12$ the dynamics are classical dilaton gravity, and where $e^{-2varphi} ll N/12$ they reduce to Liouville gravity coupled to matter, whose $T_{+-}$ constraint forces the curvature to vanish and whose Bondi mass, read off from the surface term in $M(sigma^-) = 2e^{lambda(sigma^+-sigma^-)}(lambda deltarho + partial_+deltavarphi - partial_-deltavarphi) + (N/12)(partial_-deltarho - partial_+deltarho)$, vanishes for every asymptotically flat state. Energy conservation across that boundary is what does the work: the incoming pulse starts with nonzero Bondi energy in the dilaton region and ends in a region where no excitation can carry energy, so the difference must have gone out as radiation. The trace-anomaly computation of the one-loop stress tensor supplies the quantitative check that the radiated energy is of the right order, and the observation that $e^{-2varphi} = N/24$ at the turnaround point is what makes the coupling weak there and the semiclassical treatment self-consistent.

Extended reading notes

Core claim

The paper's central claim is that in the large-$N$ limit of two-dimensional dilaton gravity, black holes are evanescent: they begin to form and then evaporate away before an event horizon or curvature singularity ever exists. The argument has three parts. Classically, the action $S = (1/2G)int d^2x sqrt{-g}[e^{-2varphi}(R + 4(nabla varphi)^2 + 4lambda^2) - (1/2)(nabla f)^2]$ is exactly integrable in conformal gauge, and even an arbitrarily weak matter shock wave produces a black hole metric with a horizon and singularity, which shows that weak-field perturbation theory fails because the expansion parameter $e^{varphi}$ grows without bound near the singularity. At one loop, the trace anomaly fixes the outgoing stress tensor completely, giving a Hawking flux that approaches the constant $lambda^2/48$ at late retarded time independent of mass. Because that flux cannot be integrated over all of $I^+_R$ without exceeding the initial mass, the authors include the $O(N)$ matter-induced Liouville term in the effective action and analyze the Bondi mass $M(sigma^-)$ on null surfaces. Since the Liouville region admits only zero-energy asymptotically flat states, and the pulse must eventually enter it, the Bondi mass must fall to zero while the left-moving global charge $Q_{1L} = int dsigma^+ partial_+ f_1$ is retained. The authors are explicit that this is a qualitative and partly conjectural picture rather than a solved problem.

Load-bearing premise

The argument assumes the leading-order $1/N$ effective action stays a controlled description across the boundary between the dilaton region and the Liouville region, even though the authors report that second-order perturbation theory diverges there and that they have not shown the large-$N$ equations have a well-defined evolution.

Editorial extensions

If this is right

If the picture is right, the formation and evaporation of a black hole in this model is described by an ordinary unitary evolution from $I^-$ to $I^+$, with no loss of quantum coherence and no need for a mixed final state.
The end state of collapse is a zero-energy bound state of matter that nevertheless carries global charges such as $Q_{1L}$, so the model predicts remnants distinguished by conserved quantum numbers rather than by mass.
Because the horizon and singularity of the classical solution are replaced by a region governed by Liouville gravity with vanishing curvature, the model has no interior where information could be trapped or destroyed.
The same action arises as the effective theory of the radial modes of extremal dilatonic black holes in four or more dimensions, so the result suggests that the physics of the extremal throat, not the horizon, is where the interesting quantum behavior lives.

Reading between the lines

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

The proposed endpoint behaves like a remnant, which trades the information-loss problem for a different one: a zero-energy state that can carry arbitrary global charge may be infinitely degenerate, and the paper does not address whether such states are consistent with entropy bounds.
Because the two-dimensional Hawking flux is asymptotically mass-independent, this model cannot reproduce the detailed thermodynamics of a four-dimensional hole; it tests the unitarity question in isolation, not the whole evaporation history.
The authors' own note that second-order perturbation theory diverges at the boundary between the dilaton and Liouville regions suggests a sharp, perhaps non-perturbative, transition; a numerical integration of the large-$N$ equations of motion on null surfaces is the obvious next step and would either confirm or kill the picture.
The claim that all asymptotically flat Liouville states have zero energy is close to saying the model has no local degrees of freedom left after evaporation, which would make the $S$-matrix almost trivial apart from charge labels; whether that is a feature or a defect is worth probing.

Original abstract

A renormalizable theory of quantum gravity coupled to a dilaton and conformal matter in two space-time dimensions is analyzed. The theory is shown to be exactly solvable classically. Included among the exact classical solutions are configurations describing the formation of a black hole by collapsing matter. The problem of Hawking radiation and backreaction of the metric is analyzed to leading order in a $1/N$ expansion, where $N$ is the number of matter fields. The results suggest that the collapsing matter radiates away all of its energy before an event horizon has a chance to form, and black holes thereby disappear from the quantum mechanical spectrum. It is argued that the matter asymptotically approaches a zero-energy ``bound state'' which can carry global quantum numbers and that a unitary $S$-matrix including such states should exist.

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, 4,894 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.49 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.07 · 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.

A renormalizable theory of quantum gravity coupled to a dilaton and conformal matter in two space-time dimensions is analyzed. The theory is shown to be exactly solvable classically. Included among the exact classical solutions are configurations describing the formation of a black hole by collapsing matter. The problem of Hawking radiation and backreaction of the metric is analyzed to leading order in a $1/N$ expansion, where $N$ is the number of matter fields. The results suggest that the collapsing matter radiates away all of its energy before an event horizon has a chance to form, and black holes thereby disappear from the quantum mechanical spectrum. It is argued that the matter asymptotically approaches a zero-energy ``bound state'' which can carry global quantum numbers and that a unitary $S$-matrix including such states should exist.

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	A renormalizable theory of quantum gravity coupled to a dilaton and conformal matter in two space-time dimensions is analyzed.	contribution 0.74	0.78	0.02	asserted 0.86
s1	The theory is shown to be exactly solvable classically.	result 0.84	0.90	0.03	asserted 1.00
s2	Included among the exact classical solutions are configurations describing the formation of a black hole by collapsing matter.	result 0.75	0.81	0.03	asserted 1.00
s3	The problem of Hawking radiation and backreaction of the metric is analyzed to leading order in a $1/N$ expansion, where $N$ is the number of matter fields.	method 0.89	0.89	0.03	asserted 0.91
s4	The results suggest that the collapsing matter radiates away all of its energy before an event horizon has a chance to form, and black holes thereby disappear from the quantum mechanical spectrum.	result 0.63	0.84	0.90	hedged possibility 0.98
s5	It is argued that the matter asymptotically approaches a zero-energy ``bound state'' which can carry global quantum numbers and that a unitary $S$-matrix including such states should exist.	interpretation 0.99	0.59	0.24	hedged possibility 0.69

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

Figures

**Figure 1.** An incoming f−wave in classical dilaton gravity in the formation of a black hole. To see that this is inde ple of an f shockae traeling in the x − direction ith m

**Figure 2.** An incoming f−wave in quantum dilaton gravity

Figures reproduced from arXiv:hep-th/9111056 by the authors.

References

Works cited (11)

[1]

S. W. Hawking, “Particle creation by black holes,” Comm. Math. Phys. 43 (1975) 199

View on Pith 1975
[2]

S.W. Hawking, “Breakdown of Predictability in Gravitat ional Collapse,” Phys. Rev. D14 (1976) 2460

View on Pith 1976
[3]

For a recent review, see R. Wald’s 1991 Erice lectures , “B lack Hole Thermodynamics”, University of Chicago preprint (1991)

View on Pith 1991
[4]

G.W. Gibbons, “Antigravitating black hole solitons wit h scalar hair in N=4 super- gravity,” Nucl. Phys. B207 (1982) 337; G.W. Gibbons and K. Maeda, “Black holes and membranes in high er-dimensional theories with dilaton ﬁelds,” Nucl. Phys. B298 (1988) 741

View on Pith 1982
[5]

D. Garﬁnkle, G. Horowitz, and A. Strominger, “Charged bl ack holes in string theory,” Phys. Rev. D43 (1991) 3140; G. Horowitz and A. Strominger, “ Black strings and p-branes,” Nucl. Phys. B360 (1991) 197

View on Pith 1991
[6]

S.B. Giddings and A. Strominger, “Exact black ﬁvebranes in critical superstring the- ory,” Phys. Rev. Lett. 67 (1991) 2930

View on Pith 1991
[7]

R. Jackiw, “Liouville ﬁeld theory: a two-dimensional mo del for gravity?,” in Quantum Theory of Gravity , S. Christensen, ed. (Hilger, Bristol U.K. 1984) ; A.H. Chamseddine, “A solution to two dimensional quantum gr avity. Non-critical strings” Phys. Lett. B256 (1991) 379

View on Pith 1991
[8]

R.B. Mann, “Lower dimensional gravity,” Waterloo prepr int W ATPHYS-TH-91-07, to appear in Proc. of 4th Canadian Conf. on General Relativit y and Relativistic As- trophysics, Winnipeg, Canada

View on Pith
[9]

E. Witten, “On string theory and black holes,” Phys. Rev. D44 (1991) 314

View on Pith 1991
[10]

S. M. Christensen and S. A. Fulling, “Trace anomalies an d the Hawking eﬀect,” Phys. Rev. D15 (1977) 2088

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[11]

E. Tomboulis, “1/N expansion and renormalization in qu antum gravity,” Phys. Lett. B70 (1977) 361. 11

View on Pith 1977

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Small four-dimensional black holes in an infinite family of ghost-free higher-curvature theories have positive specific heat, effectively infinite lifetimes, and leave huge-entropy remnants.
An Investigation of AdS$_2$ Backreaction and Holography
hep-th 2016-06 conditional novelty 6.0 of 10

A two-dimensional dilaton gravity model reduces to a one-dimensional Schwarzian-derivative theory of a dynamical boundary time, exhibiting maximal Lyapunov chaos and exponential black hole evaporation.
A Self-consistent Model of the Black Hole Evaporation
hep-th 2013-02 conditional novelty 6.0 of 10

A self-consistent semiclassical solution shows a single collapsing null shell stops evaporating and leaves a horizon, while continuous null matter evaporates completely without a macroscopic horizon.
Solving the Simplest Theory of Quantum Gravity
hep-th 2012-05 conditional novelty 6.0 of 10

The worldsheet theory of a free critical bosonic string has an exact pure-phase S-matrix, e^{i s l_s^2/4}, that reproduces the known string spectrum and exhibits gravitational features such as a minimal length and a H...
Information in Black Hole Radiation
hep-th 1993-06 accept novelty 6.0 of 10

If information escapes in Hawking radiation, it does so at a rate that is non-perturbatively small, so no order-by-order expansion in M_Planck/M or 1/N can confirm or rule it out.
Asymptotic Algebras and Holography of Information in CGHS Model
hep-th 2026-06 unverdicted novelty 5.0 of 10

Establishes holography of information in the CGHS model via asymptotic algebras and argues that islands violate commutativity of left- and right-boundary algebras.
The fate of Schwarzschild--de Sitter black holes: nonequilibrium evaporation
hep-th 2025-11 conditional novelty 5.0 of 10

In the Unruh–de Sitter state the anomaly flux J=(N/48π)(κ_b²−κ_c²) is positive throughout the static patch, so every neutral SdS black hole evaporates monotonically and only the Nariai limit has zero flux.
UV Effects and Short-Lived Hawking Radiation: Alternative Resolution of Information Paradox
hep-th 2024-11 unverdicted novelty 5.0 of 10

Hawking radiation terminates around the scrambling time due to trans-Planckian stringy effects in GUP and string-field-theory-inspired toy models, yielding negligible evaporation and a mostly classical black hole.
The universality of islands outside the horizon
hep-th 2021-10 conditional novelty 5.0 of 10

For any non-extremal D-dimensional eternal black hole, a quantum extremal surface exists just outside the horizon when c·G_D is small, and the late-time radiation entropy saturates twice the Bekenstein-Hawking entropy.
Holographic moving mirrors
hep-th 2021-06 conditional novelty 5.0 of 10

Holographic duals of moving-mirror CFTs are constructed via AdS/BCFT, the kink mirror yields a Page-curve-shaped entanglement entropy, and a double-mirror setup produces a new three-way phase transition.
Replica wormholes and capacity of entanglement
hep-th 2021-05 conditional novelty 5.0 of 10

A replica path integral formula for the capacity of entanglement in JT gravity is derived and checked against the thermal heat capacity in a high temperature eternal black hole.
Observations of Hawking radiation: the Page curve and baby universes
hep-th 2020-10 conditional novelty 5.0 of 10

Replica wormholes make the Hawking radiation seen by asymptotic observers obey the Page curve, at the cost of baby-universe superselection sectors that turn the theory into an ensemble.
Pure de Sitter space and the island moving back in time
hep-th 2020-08 conditional novelty 5.0 of 10

Using the island formula on a dimensionally reduced model of pure three-dimensional de Sitter space, the entanglement entropy between the inside and outside of a cosmological horizon follows a Page curve capped at the...
Symmetries at Null Boundaries: Two and Three Dimensional Gravity Cases
hep-th 2020-07 accept novelty 5.0 of 10

In 2d and 3d gravity, surface charges at a null boundary can always be made integrable by a field-dependent change of basis, and the resulting symmetry algebra takes a universal Heisenberg-plus-diffeomorphism form.
Island in the Presence of Higher Derivative Terms
hep-th 2020-05 conditional novelty 5.0 of 10

The island formula, extended to four-dimensional higher-derivative gravity via Dong's entropy functional, still yields a Page curve for both asymptotically flat and AdS black holes.
Page Curve for an Evaporating Black Hole
hep-th 2020-04 conditional novelty 5.0 of 10

For an evaporating black hole in asymptotically flat two-dimensional dilaton gravity, the entanglement entropy of Hawking radiation follows a Page curve whose Page time is one third of the black hole lifetime.
Flat space holography and complex SYK
hep-th 2019-11 conditional novelty 5.0 of 10

A boundary action generalizing the Schwarzian is derived from two-dimensional flat space dilaton gravity and recovered from complex SYK in a scaling limit, proposing a flat space holographic correspondence.
Towards a bulk description of higher spin SYK
hep-th 2018-02 conditional novelty 5.0 of 10

The authors derive Yang-Mills and higher-spin generalizations of the Schwarzian boundary action in two-dimensional BF dilaton gravity, and compute the resulting entropy including a one-loop coefficient of -(N^2-1)/2 f...
Menagerie of AdS$\boldsymbol{_2}$ boundary conditions
hep-th 2017-08 conditional novelty 5.0 of 10

Different boundary conditions for two-dimensional JT gravity produce an sl(2) current algebra, a Virasoro algebra, a warped conformal algebra, or a u(1) algebra, with the on-shell action reducing to a Schwarzian action.
Black holes, quantum information, and unitary evolution
hep-th 2012-01 conditional novelty 5.0 of 10

Black hole unitarity can be restored by treating Hilbert-space tensor factorization, not spacetime, as fundamental, with information transferred from the black hole interior to an exterior atmosphere through minimal s...
Global geometry of two-dimensional charged black holes
hep-th 2006-04 conditional novelty 5.0 of 10

Pair creation of charged particles replaces the inner Cauchy horizon of a two-dimensional charged black hole with a spacelike singularity.
Noncommutative Two Dimensional Gravities
hep-th 2006-02 conditional novelty 5.0 of 10

The authors show that AdS2 and a two-dimensional black hole solution of commutative gravity satisfy the equations of the noncommutative gauge theory formulation, with only partial verification for the black hole.
Wald-like entropy and Islands in Dimensionally Reduced Einstein-Hilbert Gravity
hep-th 2026-07 conditional novelty 4.0 of 10

Wald-like Noether charge of the DREH plus Polyakov-Liouville action yields the island generalized entropy and unitary Page curves for eternal and quasi-stationary evaporating black holes.
Anomaly-driven evaporation endpoints of a two-dimensional regular black hole
hep-th 2026-06 unverdicted novelty 4.0 of 10

The FFN dilaton-coupled anomaly model applied to the 2D Bardeen-like black hole enforces r_∞=√2 ℓ for quiescent finite-radius branches and excludes most null branches except the borderline p=2 power-law case under str...
First Law for Nonsingular Black Holes in 2D Dilaton Gravity
gr-qc 2026-03 reject novelty 4.0 of 10

For 2D nonsingular dilaton black holes with A=f+c, the first law holds with energy E=-c/2 once the asymptotic time translation is properly normalized.
Cauchy-horizon flux coefficients in the reduced Polyakov model
gr-qc 2025-11 reject novelty 4.0 of 10

The abstract gives the inner-horizon flux coefficient F_-^∞ = t_v - Nκ_-^2/(48π) and its cancellation surface; the supplied full text instead claims a state-independent trace-anomaly enforcement of strong cosmic censo...
Note on Type $III_1$ Algebras in $ c= 1$ String Theory and Bulk Causal Diamonds
hep-th 2025-04 conditional novelty 4.0 of 10

In the c=1 string theory, finite-region operator algebras are Type III_1, but this encodes infinite-volume boundary structure rather than black hole horizons.
Effects of Non-locality in Gravity and Quantum Theory
gr-qc 2020-09 conditional novelty 4.0 of 10

Ghost-free non-local theories with scale l yield finite linearized gravitational fields, a critical opaque frequency for delta-potential scattering, and l-dependent black hole entropy while the Hawking flux is unchanged.
Notes on islands in asymptotically flat 2d dilaton black holes
hep-th 2020-04 conditional novelty 4.0 of 10

An island emerges outside the horizon of an eternal asymptotically flat 2d dilaton black hole, and the radiation entanglement entropy saturates at approximately twice the Bekenstein-Hawking entropy, reproducing the Pa...

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How later papers used it

221 later papers cite it

Evidence: substantial. 214 of the citing papers share no author with it, and 25 of those carry a confident label from Pith's citation classifier.

Pith read 22 of the 371 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 7 papers with this label

As the gravitational part $I_grav$ of the above effective action, we choose the $CGHS$ action [ref] , I_grav= 14π∫dx^2 -g (ΦR -Λ),

Evaporation of black holes in flat space entangled with an auxiliary universe (2021) · Two disjoint asymptotically flat universes · 0.92
Followed this paper and used the gauge g_+-=-1/2 exp(2ρ), g_–=g_++=0 to study its equations.

Instant Folded Strings and Black Fivebranes (2020) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

191 arXiv papers cite this in 322 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 · 169 sentences without a confident label

Builds on it 4 papers

Starting from the postcarrollian JT model introduced in the previous subsection, we perform the limit $Λ→0$ to obtain a postcarrollian version of the CGHS model [ref] in the formulation of Cangemi and Jackiw [ref] .

Postcarrollian gravity · Postcarrollian CGHS model · 0.97
For example, when we impose $α=-1/32$, $β=-1/8$, we have an $α'$-corrected Callan-Giddings-Harvey-Strominger (CGHS)-like model[Notably we have not included the $e^-2ϕ4λ^2$ contribution or the minimally coupled matter action.] [ref] : I_CGHSα' =-1/2∫d^2x√(-g)[e^-2ϕ(R+4(∇ϕ)^2) -α'/4e^-31/16ϕ(ℒ_GB+105/16ϕ(∇ϕ)^2-1635/256(∇ϕ)^4)] .

The Stringy Origins of Galileons and their Novel Limit · Galileons from Strings · 0.97
Another example would be to study ghost-free infinite-derivative modifications of the CGHS theory containing additional scalar matter fields such as the model considered in [ref] .

Ghost-free infinite-derivative dilaton gravity in two dimensions · Conclusions · 0.81

Uses its method or tool 6 papers

To comply with this requirement, we study pure de Sitter space in three dimensions by doing a dimensional reduction to two dimensions such that we are able to take into account semi-classical corrections using the conformal anomaly along the lines of Refs. [ref] .

Pure de Sitter space and the island moving back in time · Introduction · 0.98
Using this conformal anomaly [ref] the energy that reaches $ℐ^+_R$ at time $σ_out^-$ is [equation] Here we follow an alternative procedure.

Quantum fluctuating CGHS geometries and the information paradox · Energy density · 0.85
For $N≫1$ the one-loop effective action describing the semiclassical back-reaction due to this matter sector is given by adding the following conformal anomaly term to the action [ref] , S_q = - N/12 ∫d^2x √(-g) ( 1/2 R ^-1 R - 6 (∇r)^2/r^2 ^-1 R - 6 R lnr ) .

Thermodynamics of Large AdS Black Holes · One-loop action · 0.83

Uses its data or values 1 paper

We note that the Hawking temperature of a CGHS black hole is $T_H=1/2π$, independent of the black hole mass [ref] , and the Bekenstein-Hawking entropy is given by $S_BH=2 M$.

Holographic Complexity: Stretching the Horizon of an Evaporating Black Hole · Complexity of a two-sided black hole · 0.98

Compares with it 9 papers

It is straightforward to take the limit $→0$ of [ref]. Ĩ_C := lim_→0Ĩ^_2dg = -1/κ̃ ∫_ ^2 x √(|g|) (ϕ̃ R - 2a ) eq:2de9 The action $Ĩ_C$ coincides with the geometric part of the CGHS action [ref] .

Liouville gravity from Einstein gravity · Constructing the limiting action · 0.85
Now if we use these transformations in ([ref]), the form of $E^x$ will becomes exactly the same as the form it gets in the vacuum case in the conformal gauge in [ref] .

A local true Hamiltonian for the CGHS model in new variables · Gauge fixing the vacuum theory · 0.87
This is exactly the result obtained in [ref] .

Instantaneous Thermalization in Holographic Plasmas · Linear Dilaton Black Hole Formation · 0.98

Cites it as support 3 papers

This result has been derived in a study of the CGHS [ref] model by Ashtekar et al in [ref] .

Conservative solutions to the black hole information problem · Introduction · 1.00
The interpretation of entropy as a scalar function can be motivated by dimensional reduction, and has also been validated in linear dilaton models [ref] [ref] [ref] , where the variation in area comes from variation of the Planck scale at fixed string scale.

JT Gravity Coupled to Fermions · Introduction · 0.98
The analysis of [ref] shows that it's not surprising that classical physics fails for the Type 0B EFT, because validity of the classical field equations near the black hole horizon requires a large number of Ramond-Ramond fields.

Note on Type $III_1$ Algebras in $ c= 1$ String Theory and Bulk Causal Diamonds · Introduction · 0.98

Cites it as background 97 papers

In this section, we briefly review two-dimensional black holes in the RST model [ref] and the island rule to calculate the generalized entropy of Hawking radiation in the RST model.

Quantum focusing conjecture in two-dimensional evaporating black holes · 2D black holes and Islands · 0.97
The action of the model [equation] includes the classical part representing CGHS dilaton gravity [ref] and a quantum counter-term [ref] — the last term in the integrand — providing exact solvability at one-loop level.

Dilaton gravity with a boundary: from unitarity to black hole evaporation · Weyl transformation · 0.89
In the original CGHS model [ref] , the dilaton gravity sector is coupled to matter in the form of $N$ minimally coupled free scalars, with $N≫24$ so that semi-classical corrections are dominated by one-loop effects due to the matter fields.

Page Curve for an Evaporating Black Hole · Coupling to matter · 0.85

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.

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S. W. Hawking, “Particle creation by black holes,” Comm. Math. Phys. 43 (1975) 199

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S.W. Hawking, “Breakdown of Predictability in Gravitat ional Collapse,” Phys. Rev. D14 (1976) 2460

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For a recent review, see R. Wald’s 1991 Erice lectures , “B lack Hole Thermodynamics”, University of Chicago preprint (1991)

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G.W. Gibbons, “Antigravitating black hole solitons wit h scalar hair in N=4 super- gravity,” Nucl. Phys. B207 (1982) 337; G.W. Gibbons and K. Maeda, “Black holes and membranes in high er-dimensional theories with dilaton ﬁelds,” Nucl. Phys. B298 (1988) 741

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D. Garﬁnkle, G. Horowitz, and A. Strominger, “Charged bl ack holes in string theory,” Phys. Rev. D43 (1991) 3140; G. Horowitz and A. Strominger, “ Black strings and p-branes,” Nucl. Phys. B360 (1991) 197

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S.B. Giddings and A. Strominger, “Exact black ﬁvebranes in critical superstring the- ory,” Phys. Rev. Lett. 67 (1991) 2930

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R. Jackiw, “Liouville ﬁeld theory: a two-dimensional mo del for gravity?,” in Quantum Theory of Gravity , S. Christensen, ed. (Hilger, Bristol U.K. 1984) ; A.H. Chamseddine, “A solution to two dimensional quantum gr avity. Non-critical strings” Phys. Lett. B256 (1991) 379

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R.B. Mann, “Lower dimensional gravity,” Waterloo prepr int W ATPHYS-TH-91-07, to appear in Proc. of 4th Canadian Conf. on General Relativit y and Relativistic As- trophysics, Winnipeg, Canada

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E. Witten, “On string theory and black holes,” Phys. Rev. D44 (1991) 314

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S. M. Christensen and S. A. Fulling, “Trace anomalies an d the Hawking eﬀect,” Phys. Rev. D15 (1977) 2088

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E. Tomboulis, “1/N expansion and renormalization in qu antum gravity,” Phys. Lett. B70 (1977) 361. 11

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