The Stretched Horizon and Black Hole Complementarity

J. Uglum; L. Susskind; L. Thorlacius

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The Stretched Horizon and Black Hole Complementarity

L. Susskind, L. Thorlacius, J. Uglum

High Energy Physics - Theory · Submitted 16 Jun 1993 · 30 references

Pith's verdict: The origin point for the modern stretched-horizon picture, with checkable 2D results and one honest gap in §3.4 that the paper papers over with an assertion.

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arXiv IDhep-th/9306069 (version 2)

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CitationJ. Uglum, L. Susskind, L. Thorlacius. "The Stretched Horizon and Black Hole Complementarity." arXiv:hep-th/9306069 (1993). https://pith.science/paper/PGKZI2FU

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Editor's note

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Worth your time, and worth citing — but read it as a framework paper, not a derivation. What is actually new: the stretched horizon moves from a macroscopic membrane (Thorne–Price–MacDonald) to one Planck area out (Eq. 3.1, 3.16), and it gets a quantum-mechanical reading — exp(A) states, coarse-grained into the dissipative membrane. Complementarity is stated as an explicit principle rather than gestured at. The 2D work is real and checkable: the area equation with its friction term (3.8, 3.28) follows from the RST solution (2.39) plus the horizon condition; the 4π resistance falls out of (3.14); the area random walk (4.7) is cross-checked against the thermodynamic variance. I followed each step. The big soft spot is the one the paper names itself: the argument that the joint interior–exterior state on Σ_P is operationally meaningless is asserted, not derived, and the paper concedes a global QFT of gravity would falsify its postulates. That is the load-bearing premise and it stays a premise. The stress-test's §3.4 point holds up on reading. Eq. 3.41 gives ω_in = ∫_{σ+}^{∞} du e^{σ+−u} T++(u) — an integral over flux that has not arrived yet — and the kernel W in (3.43) carries the Θ(u−σ+) branch. So the dressing is future-dependent by construction, and the claim that this “does not preclude a conventional causal Hamiltonian description” is an assertion, not a construction. That is a real gap against Postulate 1's finite-time Hamiltonian. It is a gap in a supporting argument, not in complementarity itself; the teleology is inherited from the membrane paradigm and from the fact that event horizons are globally defined. Flag it, do not reject over it. Minor: §4 leans on [28], work in progress, and says so (“has not been rigorously established”). §5's Planck-scale “atoms” at fixed surface density are proposed without dynamics, which the authors also say. Who it is for: anyone working on the information paradox, horizon thermodynamics, or the emergence of spacetime from quantum mechanics. It is the origin point for a picture that is still the default. Peer review: yes, send it out. It is a framework paper with checkable 2D results and an honest statement of what is assumed. The referee should press on §3.4 and on whether the operational argument can be turned into a theorem.

Referee report

Significance

The paper is a foundational statement of black hole complementarity and of the stretched-horizon/membrane program, and it is likely to be widely cited and widely taught. Its strengths are concrete: the two-dimensional derivations are explicit and checkable, the area equation with its dissipative term follows from the RST solution (2.39) together with the horizon condition (3.16), the resistivity follows from the boundary condition (3.14), and the thermodynamic fluctuation estimate (4.7) is independently cross-checked against the field-theoretic estimate (4.13). The energy-conservation argument of Eq. (3.52), which removes the need for the negative-energy 'thunderpop' of the earlier RST analysis, is a genuine improvement, and the discussion of entanglement versus thermal entropy in §5.2 yields a falsifiable expectation — long-time non-thermal correlations and no stable remnants — rather than a purely verbal resolution. If the framework holds, it reframes the information paradox as a question about which observables are jointly meaningful rather than about whether information is lost.

Major objections (2)

[§3.4, Eqs. (3.41)–(3.43)] This section is offered as the resolution of the teleological boundary condition of §3.1, and it explicitly claims that the future-dependence 'does not preclude a conventional causal Hamiltonian description of the quantum stretched horizon.' The construction given does not establish that claim. In Eq. (3.41), ω_in = (P∞ − P+(σ+))e^{σ+} + M(σ+), and with P+(σ+) = ∫_{−∞}^{σ+} du e^{−u} T++(u) the first term equals e^{σ+}∫_{σ+}^{∞} du e^{−u} T++(u), an integral over infalling flux at later σ+. Equivalently, the kernel W in Eq. (3.43) contains the branch Θ(u−σ+)e^{σ+−u}, which is nonzero for σ+ < u. The dressing at a given σ+ therefore depends on matter that has not yet arrived, which is precisely the teleology the section claims to remove; relabeling it a 'dressing' does not supply the finite-time Hamiltonian asserted in Postulate 1. Either exhibit the Hamiltonian and the enlarged state space on which it acts, or state plainly that the causal description is recovered only for the coarse-grained thermodynamic variables and not at the level of the fundamental Hamiltonian.
[§1, paragraph beginning 'Although this conclusion seems to follow from fairly general principles'] The load-bearing premise of the paper is that a state on Σ_P in H_bh ⊗ H_out is operationally meaningless, and the authors are commendably explicit that this is an assumption rather than a derivation: they concede that 'if this is the case, such a quantum field theory is inconsistent with our postulates,' and in §5.3 that 'precisely what is wrong is not clear to us.' Because the limitation is acknowledged, the remaining issue is not that the premise is unproved but that the manuscript supplies no criterion for when the tensor-product description is supposed to fail. Without such a criterion the postulates are conditional in a way that cannot be tested against a candidate global quantum field theory of gravity, since any such theory can be excluded by fiat. A concrete test would be to name an observable computed in H_bh ⊗ H_out whose value differs from the complementarity prediction, or to state the operational condition under which the joint description is declared inadmissible. As written, the central claim is a proposal for how the paradox could be dissolved, not a demonstration that it is.

Minor objections (8)

[Eq. (2.20)] Both lines of Eq. (2.20) print the same expression, t = σ = (1/2)log(−y+y−). The spatial tortoise coordinate should presumably be σ = (1/2)log(−y+/y−), so that σ± = t ± σ reproduces y± = ±e^{σ±}. Please correct.
[Eq. (3.15)] The argument of the logarithm, 1 − y−P∞, does not obviously follow from the solution (2.39), where the corresponding term is log(−y+(y− − P∞)). Please check the sign and the factor of y+.
[§3.3] The statement that 'the process must also destroy the conservation of quantum numbers' sits awkwardly with Postulate 1's unitary S-matrix, which conserves global charges. The intended statement appears to be that the charges are carried out by many soft quanta over a long time rather than reflected promptly; please rephrase to avoid the appearance of charge non-conservation.
[§4, Eqs. (4.5)–(4.7)] For a two-dimensional black hole the specific heat is infinite, so Eq. (4.5) gives an infinite variance, while Eq. (4.7) quotes a finite diffusion coefficient. The text reconciles these by distinguishing equilibrium from time-dependent evolution and by computing (4.7) from the surrounding bath, but a sentence making that distinction explicit at the point where (4.5) is applied would prevent the reader from reading the two results as contradictory.
[Abstract and §1] 'course graining' should read 'coarse graining'.
[§2.3] 'Russo, Susskin d and Thorlacius' should read 'Russo, Susskind and Thorlacius'.
[References] Ref. [9] reads 'P Black Holes: The Membrane Paradigm' with a stray 'P', and Ref. [17] has a doubled comma after 'Thorlacius'.
[Figures 6 and 7] The text refers to t0, t*, and tf, but the figures are described only in prose; a caption listing which curve is γ_cr, which is H_S, and where each time label sits would make the sequence of events much easier to follow.

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The paper

The paper claims

A black hole can evaporate unitarily for a distant observer and still let a freely falling observer pass the horizon without noticing anything, because no experiment can compare the two accounts.

The reading

The paper confronts the standard argument that unitary evaporation and a smooth horizon cannot both be true. That argument runs: if the outgoing radiation is pure, the state on a spacelike surface that crosses the horizon must factorize, forcing the interior state to be the same regardless of what fell in, which violates the equivalence principle. The authors reply that such a factorized state is not physically meaningful, since no observer can measure both factors, and they build a description from the outside only. They lay down three postulates: a unitary $S$-matrix for the distant observer, ordinary semi-classical field equations outside the horizon, and a horizon Hilbert space of dimension $e^{S(M)}$ with $S$ the Bekenstein entropy. Working in a solvable two-dimensional dilaton-gravity model, they show these postulates are realized by a stretched horizon, a timelike surface about one Planck unit of area outside the global horizon that absorbs infalling matter, heats to a mass-independent local temperature, and re-radiates it.

What carries the argument

The stretched horizon is defined by mapping each point of the global event horizon backward along an ingoing null ray to the point where the area function is larger by a fixed amount $A(m)+d$; in the semi-classical two-dimensional model the natural choice is $-y^+y^- = k/4$, giving a surface at fixed tortoise coordinate $s_S = 1/2 log(k/4)$ that is only minimally outside the true horizon. Its dynamics are carried by the area equation $d^2A_S/dt^2 - dA_S/dt = -T_{++} + k/4$, whose second term is the dissipative, time-asymmetric piece and whose right side balances incoming flux against outgoing Hawking flux. Absorption is modelled by a boundary condition on the matter field equivalent to a surface resistivity of $4p$ (377 ohms in four dimensions), and the horizon's entropy is identified with its area, so the dimension of its Hilbert space is $e^{A}$. Fluctuations are captured by the free-field behaviour of the area perturbation, giving $< (A(t)-A_0)^2 > = (N/24p^2) t$, matching the thermodynamic estimate from the specific heat.

Extended reading notes

Core claim

The central claim is a principle of black hole complementarity: the interior and exterior of a black hole are not two parts of one measurable world but two descriptions suited to two classes of observer, and the state that would describe both at once has no operational content. If that is granted, the contradiction dissolves, and a distant observer may see a unitary $S$-matrix while an infalling observer sees nothing at the horizon. The paper's constructive half is that the thermodynamics of the stretched horizon is not fundamental but arises from coarse-graining a large, ergodic set of horizon degrees of freedom whose number is fixed by the area. In the two-dimensional model the authors write an explicit equation for the horizon area that contains a friction-like term, identify the membrane's absorption with a resistivity of $4$, compute the onset of Hawking emission as an excitation of the horizon that precedes the arrival of the infalling matter, and show that the horizon area undergoes Brownian motion with variance growing linearly in time. They conclude that the information returns in long-time, non-thermal correlations spread across the whole emission history, not in late low-energy quanta and not in a stable remnant.

Load-bearing premise

The load-bearing premise is that a quantum state describing the inside and the outside of a black hole at once is physically meaningless because no single observer can measure both halves; the paper argues this operationally and concedes that a quantum field theory of gravity might supply such a global state anyway, in which case its own postulates would be the thing that fails.

Editorial extensions

If this is right

Information about the infalling state is returned in long-time correlations between Hawking quanta emitted at very different times, so the radiation is thermal in every local respect but not globally.
There is no stable or long-lived remnant: the entanglement entropy of the radiation is bounded by the horizon area and must return to zero as the horizon shrinks back to its vacuum size.
The horizon area random-walks away from its classical trajectory, so the lifetime of a black hole of mass $M$ carries an intrinsic spread of order $\sqrt{M}$.
The local temperature at the stretched horizon is of order the Planck temperature and independent of the black hole mass, which implies a universal, mass-independent surface density of horizon degrees of freedom.
The negative-energy 'thunderpop' that the semi-classical model needs at the endpoint is replaced by a smooth cooling in which temperature and luminosity go to zero rather than overshooting.
Near-critical incoming flux is a regime where mean-field semi-classical reasoning should fail, in analogy with critical phenomena, with horizon fluctuations growing without bound.

Reading between the lines

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

If complementarity is correct, 'the interior' is better read as a bookkeeping device than as a place, and any proposed experiment that claims to compare an infalling record with an external one must fail for a reason locatable in the theory of measurement rather than in gravitational dynamics.
The claim of one horizon state per Planck area, independent of mass, is a concrete counting target that any candidate quantum gravity can be checked against without needing the full evaporation history.
The predicted linear-in-time diffusion of horizon area suggests an observational handle: stochasticity in the emitted flux beyond what a mean-field semi-classical treatment predicts would be evidence for the coarse-grained picture over the smooth one.
The paper's own concession that a quantum field theory of gravity might supply a global Hilbert space across the horizon marks the exact seam where a future calculation could decide the issue, since such a theory would make the complementarity move unavailable.

Original abstract

Three postulates asserting the validity of conventional quantum theory, semi-classical general relativity and the statistical basis for thermodynamics are introduced as a foundation for the study of black hole evolution. We explain how these postulates may be implemented in a ``stretched horizon'' or membrane description of the black hole, appropriate to a distant observer. The technical analysis is illustrated in the simplified context of 1+1 dimensional dilaton gravity. Our postulates imply that the dissipative properties of the stretched horizon arise from a course graining of microphysical degrees of freedom that the horizon must possess. A principle of black hole complementarity is advocated. The overall viewpoint is similar to that pioneered by 't~Hooft but the detailed implementation is different.

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, 4,854 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.33 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.85 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

Three postulates asserting the validity of conventional quantum theory, semi-classical general relativity and the statistical basis for thermodynamics are introduced as a foundation for the study of black hole evolution. We explain how these postulates may be implemented in a ``stretched horizon'' or membrane description of the black hole, appropriate to a distant observer. The technical analysis is illustrated in the simplified context of 1+1 dimensional dilaton gravity. Our postulates imply that the dissipative properties of the stretched horizon arise from a course graining of microphysical degrees of freedom that the horizon must possess. A principle of black hole complementarity is advocated. The overall viewpoint is similar to that pioneered by 't~Hooft but the detailed implementation is different.

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	Three postulates asserting the validity of conventional quantum theory, semi-classical general relativity and the statistical basis for thermodynamics are introduced as a foundation for the study of black hole evolution.	contribution 0.61	0.75	0.06	asserted 0.96
s1	We explain how these postulates may be implemented in a ``stretched horizon'' or membrane description of the black hole, appropriate to a distant observer.	method 0.55	0.83	0.08	hedged possibility 0.99
s2	The technical analysis is illustrated in the simplified context of 1+1 dimensional dilaton gravity.	method 0.98	0.69	0.03	asserted 0.98
s3	Our postulates imply that the dissipative properties of the stretched horizon arise from a course graining of microphysical degrees of freedom that the horizon must possess.	interpretation 0.92	0.78	0.30	asserted 0.99
s4	A principle of black hole complementarity is advocated.	contribution 0.85	0.67	0.42	asserted 0.64
s5	The overall viewpoint is similar to that pioneered by 't~Hooft but the detailed implementation is different.	background 0.85	0.27	0.08	asserted 0.98

What kind of paper the classifier reports this is: position or commentary 0.61 · evidence from argument 0.58.

What was examined, and what was not

sources read

arXiv listing abstract v2

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.** Foliate the spacetime with a family of space-like C

**Figure 2.** FIGURE 2. Penrose diagram for the eternal black hole solutio

**Figure 3.** FIGURE 3. Penrose diagram for the infall solution.

**Figure 4.** FIGURE 4. Semi-classical black hole formation and evaporat

**Figure 5.** FIGURE 5. Construction of the classical stretched horizon.

**Figure 6.** FIGURE 6. Black hole evolution in tortoise coordinates.

**Figure 7.** FIGURE 7. Sub-critical flux of incident matter.

**Figure 8.** FIGURE 8. Thermal entropy of stretched horizon and radiatio

**Figure 9.** FIGURE 9. Entanglement entropy of radiation and stretched h

Figures reproduced from arXiv:hep-th/9306069 by the authors.

References

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Black Hole Entanglement and Quantum Error Correction
hep-th 2012-11 conditional novelty 7.0 of 10

Using quantum error-correcting codes, the authors reconstruct black hole interior observables that make the horizon look like a smooth local vacuum, provided the black hole entropy stays below the Bekenstein-Hawking bound.
An Infalling Observer in AdS/CFT
hep-th 2012-11 conditional novelty 7.0 of 10

Local bulk operators behind an AdS black hole horizon can be written as boundary CFT operators by pairing each boundary mode with a state-dependent 'tilde' partner, giving a smooth horizon at leading order in 1/N.
Towards the fast scrambling conjecture
hep-th 2011-11 accept novelty 7.0 of 10

Subject to a norm constraint on interaction terms, no Hamiltonian with dense two-body interactions can scramble quantum information faster than logarithmically in the number of degrees of freedom.
Dissipative Effects in the Worldline Approach to Black Hole Dynamics
hep-th 2005-11 accept novelty 7.0 of 10

A worldline effective field theory with multipole correlators matched to known black hole absorption cross sections reproduces horizon dissipation and predicts the leading absorptive correction to binary inspiral and ...
Non-supersymmetric smooth geometries and D1-D5-P bound states
hep-th 2005-04 conditional novelty 7.0 of 10

Smooth non-supersymmetric D1-D5-P solitons exist, form a two-integer family, and their conserved charges reproduce those of spectral-flowed CFT states.
The black hole final state
hep-th 2003-10 conditional novelty 7.0 of 10

A unique final-state boundary condition at the black hole singularity, combined with the entanglement of Hawking pairs, makes evaporation unitary by teleporting infalling information into the outgoing radiation.
Eternal Black Holes in AdS
hep-th 2001-06 conditional novelty 7.0 of 10

The maximally extended AdS black hole is dual to two copies of the boundary CFT in the thermofield double entangled state, and summing over geometries restores unitarity.
D-brane Approach to Black Hole Quantum Mechanics
hep-th 1996-02 conditional novelty 7.0 of 10

A D-brane and open-string model of a near-extremal five-dimensional Reissner-Nordström black hole reproduces the Bekenstein-Hawking entropy, the Hawking temperature, and a thermal emission spectrum from state counting alone.
Journey to the Center of a Black Hole
hep-th 2026-09 conditional novelty 6.0 of 10

An infalling correlator in BTZ diverges at the singularity, and a tower with Hagedorn growth produces an interior Hagedorn transition that is parametrically separated from the horizon in large black holes.
Investigation of the black-hole quantum atmosphere from the effective proper temperature
hep-th 2026-08 conditional novelty 6.0 of 10

Using a proper temperature derived from the conformal anomaly, the authors show that the maximum of the effective temperature, which sets the quantum atmosphere radius, approaches 1.41 times the horizon radius in the ...
The black hole S-matrix in gauge/gravity duality
hep-th 2026-07 conditional novelty 6.0 of 10

A unitary black hole S-matrix is built in AdS/CFT via collapsing brane shells; the black hole decays by exponentially rare brane emission, and the emitted branes are argued to be the original constituents, resolving t...
Macroscopic Black-Hole Remnants in a Nonlocal Field Theory: Towards Hawking Radiation in SFT
hep-th 2026-06 unverdicted novelty 6.0 of 10

In a smeared massless scalar on dynamical black hole, outgoing particle number drops to zero after scrambling time due to SFT nonlocality, implying macroscopic remnant.
Cosmological brick walls & quantum chaotic dynamics of de Sitter horizons
hep-th 2026-03 unverdicted novelty 6.0 of 10

Brick-wall spectra in de Sitter space show long-range chaotic signatures via spectral form factor and Krylov complexity even when conventional level repulsion is absent.
Entanglement inequalities, black holes and the architecture of typical states
hep-th 2025-11 unverdicted novelty 6.0 of 10

Typical states in large-N holographic CFTs exhibit UV and IR length scales set by energy and charges, producing factorization that isolates black holes via a corona of saturated entanglement wedges and extends ETH to ...
A Quantum Superposition of Black Hole Evaporation Histories: Recovering Unitarity
gr-qc 2025-07 conditional novelty 6.0 of 10

A controlled-squeezing toy model of black hole evaporation with quantum back-reaction is unitary, and the initial black hole state can be recovered from the final radiation.
Stretched Horizon Dissipation and the Fate of Echoes
hep-th 2025-06 conditional novelty 6.0 of 10

A microscopic estimate shows infalling modes with frequency near the Hawking temperature suffer only moderate dissipation before reaching a stretched horizon, so gravitational wave echoes could survive.
Quantum Schwarzschild-(A)dS Black Holes: Unitarity and Singularity Resolution
hep-th 2025-02 conditional novelty 6.0 of 10

Unitarity in unimodular time self-adjointness resolves the Schwarzschild-(A)dS singularity and yields a quantum-corrected metric interpolating between black and white hole states.
Von Neumann Algebras in Double-Scaled SYK
hep-th 2024-03 unverdicted novelty 6.0 of 10

Double-scaled SYK chord algebra is a Type II₁ factor whose empty state is tracial, cyclic, and separating.
The Price of Curiosity: Information Recovery in de Sitter Space
hep-th 2021-03 conditional novelty 6.0 of 10

In a two-dimensional de Sitter toy model, an observer who collects Hawking radiation can in principle recover information from behind the cosmological horizon, but the required backreaction forms a singularity that ev...
An Information Paradox and Its Resolution in de Sitter Holography
hep-th 2021-03 conditional novelty 6.0 of 10

In the DS/dS holographic framework, the entanglement entropy of a de Sitter subregion follows a time-dependent Page curve once entanglement islands are included, with a massless graviton.
Geometric secret sharing in a model of Hawking radiation
hep-th 2020-03 conditional novelty 6.0 of 10

Giving an end-of-the-world brane its own holographic dual black hole and letting RT surfaces cross the brane reproduces the Page curve and yields a geometric secret-sharing scheme in Hawking radiation.
Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information
hep-th 2020-02 accept novelty 6.0 of 10

Spacetime wormholes make the dimension of the dual Hilbert space a random variable, and the resulting null states enforce a Bekenstein-Hawking entropy bound in every member of the ensemble.
T-Witts from the horizon
hep-th 2020-02 accept novelty 6.0 of 10

Near a generic null hypersurface in Einstein gravity, the surface charges generate a two-tower T-Witt algebra (superrotations plus BMS3-type supertranslations), with the non-integrable part identified as horizon flux.
Chaos and complementarity in de Sitter space
hep-th 2020-02 conditional novelty 6.0 of 10

A single-sided out-of-time-order correlator in the three-dimensional de Sitter static patch decays exponentially with Lyapunov exponent 2π/β, saturating the chaos bound, while the standard double-sided configuration d...
Unitarity From a Smooth Horizon?
hep-th 2019-11 conditional novelty 6.0 of 10

Applying the Ryu-Takayanagi prescription to a semiclassically evolved bulk with a Dyson-sphere detector reproduces the Page curve, but the authors argue this is consistent with unitary boundary evolution only if semic...
Spacetime structure near generic horizons and soft hair
hep-th 2019-08 conditional novelty 6.0 of 10

A family of horizon boundary conditions labeled by s yields BMS-like algebras with spin-s supertranslations, while another choice gives a non-linear Heisenberg-like algebra whose generators build the BMS-like ones.
On Reflectivity of Quantum Black Hole Horizons
hep-th 2019-05 conditional novelty 6.0 of 10

Quantum black hole horizons reflect incoming radiation with a universal Boltzmann-factor reflectivity, exp(-ℏ|ω|/kT_H), according to three heuristic arguments.
Entanglement Wedge Reconstruction and Entanglement of Purification
hep-th 2018-04 conditional novelty 6.0 of 10

A new measure called differential purification, built from a generalization of entanglement of purification, reconstructs the bulk curve segments inside an AdS-Rindler wedge that entanglement entropy alone cannot reach.
String Theory of Supertubes
hep-th 2017-05 accept novelty 6.0 of 10

A tilted null gauging of a Wess-Zumino-Witten model yields exact worldsheet string theories for NS5-P and NS5-F1 supertubes, reproducing known supergravity solutions and exposing string-scale topology at the brane source.
Soft Heisenberg hair on black holes in three dimensions
hep-th 2016-03 conditional novelty 6.0 of 10

Near-horizon boundary conditions for 3d AdS black holes yield two affine u(1) current algebras (a Heisenberg algebra) whose charges are zero-energy soft hair that do not change the Bekenstein-Hawking entropy.
Comments on the Necessity and Implications of State-Dependence in the Black Hole Interior
hep-th 2015-03 conditional novelty 6.0 of 10

State-dependent bulk-boundary operators are necessary to describe a smooth black hole interior in AdS/CFT, including the eternal black hole, and they reproduce ordinary effective field theory for an infalling observer.
Entanglement is not Enough
hep-th 2014-11 conditional novelty 6.0 of 10

The volume of a black hole's Einstein-Rosen bridge grows in proportion to the quantum complexity of the dual state, and counting causal patches weighted by entropy reproduces that complexity including its dimension-de...
Unitarity of black hole evaporation in final-state projection models
hep-th 2013-08 conditional novelty 6.0 of 10

The Horowitz-Maldacena final-state projection model evades the AMPS firewall argument by permitting polygamous entanglement, with unitarity violations of order exp(-S_BH/2) for generic boundary conditions.
Firewalls From Double Purity
hep-th 2013-08 conditional novelty 6.0 of 10

The firewall paradox follows from the incompatibility of the infalling vacuum's purity with the purity of the outgoing Hawking radiation, independent of black hole age or entanglement, so Hilbert-space identifications...
An Apologia for Firewalls
hep-th 2013-04 conditional novelty 6.0 of 10

Identifying a black hole's interior with the early Hawking radiation, or adding nonlocal interactions to remove the firewall, does not work without abandoning standard quantum mechanics.
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.
Time Dependence of Hawking Radiation Entropy
hep-th 2013-01 conditional novelty 6.0 of 10

For a large non-rotating black hole emitting only photons and gravitons, the Hawking radiation's von Neumann entropy peaks at about 59.75% of the initial Bekenstein-Hawking entropy, at about 53.81% of the total evapor...

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How later papers used it

349 later papers cite it

Evidence: substantial. 335 of the citing papers share no author with it, and 14 of those carry a confident label from Pith's citation classifier.

Pith read 40 of the 506 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

1 later paper by other authors is listed below: 1 used its method or tool. 1 more paper by the same authors is listed: 1 cited it as support.

Uses its method or tool 1 of 2 papers with this label

Performed two thought experiments introduced by Susskind and Thorlacius to explore the validity of black hole complementarity for the black hole.

Validity of black hole complementarity in an accelerating Schwarzschild black hole (2024) · 0.84 · paraphrased: the licence does not allow quoting

Cites it as support 1 of 6 papers with this label · 1 by the same authors

By the same authors

Said that its results offer support to the black hole complementarity paradigm for solving the black hole information problem.

Quantum Chaos and Unitary Black Hole Evaporation (2022) (same authors) · 0.96 · paraphrased: the licence does not allow quoting

How the literature uses it

300 arXiv papers cite this in 450 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 · 253 sentences without a confident label

Contests it 1 paper

[ref] which addresses it in part with: “From a formal point of view, the cause of the horizon expansion is a gravitational dressing which is attached to the incoming energy flux.” However, in our scenario the horizon expansion starts in a flat, static environment, which has been unchanged for thousands of years, about one year before the shell starts to collapse and hence no incoming energy flux exists to carry a “gravitational dressing” which can be “the cause of the horizon expansion.”

Black Hole Complementarity and Violation of Causality · Massive shell collapsing on a billiard ball · contest 0.72

Uses its method or tool 2 papers

We then explore the validity of BHC for the black hole by performing two thought experiments introduced by Susskind and Thorlacius [ref] , and Hayden and Preskill [ref] .

Validity of black hole complementarity in an accelerating Schwarzschild black hole · Introduction · 0.84
For technical simplicity, we follow [ref] and take the stretched horizon of an RST black hole formed by shockwave collapse to coincide with the apparent horizon during the period of evaporation.

Action Complexity for Semi-Classical Black Holes · Evaporating Black Hole · 0.84

Compares with it 6 papers

[ref] ) focus on matter falling into an existing BH horizon whereas here we consider matter engulfed by an expanding horizon.

Black Hole Complementarity and Violation of Causality · Massive shell collapsing on a billiard ball · 0.96
The stretched horizon of black hole complementarity is placed at a Planck distance from the event horizon so that distant observers see an apparently real membrane on it [ref] , whereas our stretched horizon behaves as a membrane only approximately.

Islands and stretched horizon · Discussions · 0.99
[ref] considered experiments that ran for much shorter times than ours, though such times were always at least logarithmically longer than the light-crossing time of the black hole.

Holographic Thought Experiments · Experiments inside Black Holes · 1.00

Cites it as support 6 papers

Thus the fixed observer and free-fall observer see extremely different degrees of freedom at the horizon, which means that black hole complementarity [ref] still holds for gravity's rainbow.

Hawking, Fiducial, and Free-fall Temperatures of Black Hole on Gravity's Rainbow · Conclusion and discussion · 0.97
This conforms to the earlier idea that black hole evolution obeys the standard rules of quantum mechanics—and hence is unitary—when viewed by an external observer [ref] .

Black Hole and de Sitter Microstructures from a Semiclassical Perspective · Introduction and Summary · 0.97
These results offer support to the black hole complementarity paradigm for solving the black hole information problem [ref] .

Quantum Chaos and Unitary Black Hole Evaporation · Conclusions · 0.96

Cites it as background 155 papers

To resolve the information loss paradox, the idea of black hole complementarity (BHC) was introduced as an attempt to reconcile quantum mechanics with the equivalence principle of general relativity [ref] .

Validity of black hole complementarity in an accelerating Schwarzschild black hole · Introduction · 0.88
Black hole (BH) complementarity [ref] has been the most popular vehicle deployed to address the BH information paradox.

Black Hole Complementarity and Violation of Causality · Introduction · 0.98
According to black hole complementarity, there is no consistent way of describing both the inside and the outside of the black hole horizon [ref] .

Critical Reviews of Causal Patch Measure over the Multiverse · Black Hole Complementarity · 0.94

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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