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REVIEW 3 major objections 4 minor 45 references

Horizon partons form LLL states on a Berry monopole and, once links condense, turn the classical fictitious membrane into a physical current source with frequency- and helicity-dependent reflection.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-07-14 10:48 UTC pith:H5YOKHWW

load-bearing objection Solid technical extension of Chu's matrix black-hole model that derives LLL currents and a locking mechanism, but Ohmic recovery is phenomenological and the locking control for reflectivity frequencies is not fully closed. the 3 major comments →

arxiv 2607.10561 v1 pith:H5YOKHWW submitted 2026-07-12 hep-th cond-mat.othergr-qchep-ph

Quantum Horizon and Quantum Membrane Paradigm from Black Hole Quantum Mechanics

Chong-Sun Chu This is my paper
classification hep-th cond-mat.othergr-qchep-ph
keywords quantum membrane paradigmfuzzy sphereBerry monopolelowest Landau levelhorizon partonslink condensateHall conductivityblack-hole echoes
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper claims that a quantum black hole, already modeled as a fuzzy sphere plus a half-filled Fermi sea of fundamental partons, carries an intrinsic Berry monopole. The partons therefore sit in the lowest Landau level rather than free two-dimensional motion; their guiding-center drift produces Ohmic, Hall and polarization surface currents. When the black-hole block is coupled to an exterior Maxwell block by bifundamental link matrices, those links become tachyonic in a thin shell outside the sphere and condense. The condensate locks the world-volume gauge field to the boundary value of the exterior field, so the parton currents become genuine sources for exterior observers. The resulting boundary condition generalizes the classical ingoing membrane condition by adding explicit frequency-dependent polarization and charge-dependent Hall corrections, which in turn generate a nonzero, helicity-dependent reflection coefficient. A sympathetic reader cares because the construction replaces a bookkeeping device with microscopic degrees of freedom whose transport coefficients could leave observable imprints (echoes, polarization rotation) on near-horizon electromagnetic waves.

Core claim

Off-diagonal link modes become tachyonic near the fuzzy sphere and condense, locking the horizon gauge field b_A to the exterior Maxwell boundary value a_A; the LLL parton current thereby becomes a physical boundary source whose Ohmic, Hall and polarization components yield a frequency- and helicity-dependent reflection coefficient that generalizes the classical membrane boundary condition.

What carries the argument

Bifundamental link condensate: the tachyonic instability of off-diagonal matrix modes in a thin shell of proper thickness ~l_P outside the fuzzy sphere produces a Higgs-like potential that forces b_A = a_A, converting the world-volume LLL current into a source for the exterior Maxwell field.

Load-bearing premise

The Ohmic conductivity recovers the classical universal value 1/4π only after a phenomenological friction coefficient is conjectured to take a specific numerical value; without that conjecture the classical membrane law is not reproduced.

What would settle it

Measure the near-horizon electromagnetic reflection coefficient (or the associated echo delay and helicity-dependent polarization rotation) for a charged black hole; if the observed frequency dependence fails to match the model’s σ_xx + i(ω D ± σ_H) admittance, or if no Hall splitting appears for nonzero charge, the locking-plus-LLL claim is falsified.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The classical perfectly absorbing horizon is replaced by a quantum surface with nonzero, frequency-dependent reflectivity R_± controlled by polarization D and Hall conductivity σ_H.
  • Charged black holes induce a horizon Kerr rotation that converts linear incident polarization into rotated elliptical polarization, with rotation angle ≈ -2π σ_H.
  • Electromagnetic waves can bounce repeatedly between the reflective quantum horizon and the photon-sphere barrier, producing a train of delayed echoes whose spectrum is fixed by the microscopic transport coefficients.
  • The same locking mechanism converts any world-volume stress tensor of the LLL partons into a gravitational membrane boundary condition once the off-diagonal blocks condense.

Where Pith is reading between the lines

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

  • Because the reflection coefficient is derived rather than postulated, existing echo searches can be re-analyzed with a two-parameter (σ_H, D) template, reducing model uncertainty and sharpening exclusion limits.
  • The open-string interpretation of the bifundamental condensate suggests a possible brane construction that would embed the entire matrix model in string theory and fix the remaining free parameters a_0, a_2, q.
  • If an interior matrix block is added, the three-block interaction vertices may realize a horizonless microstate geometry whose coarse-grained limit still reproduces the same LLL membrane currents.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper constructs a microscopic quantum membrane paradigm from a non-supersymmetric matrix quantum mechanics of black holes. A quantum black hole is identified with a fuzzy sphere of rank N plus a half-filled Fermi sea of fundamental fermions (horizon partons). The topology of the fuzzy sphere induces a Berry monopole of charge J=(N-1)/2; the partons, being fundamentals, occupy the associated Lowest Landau Levels and undergo guiding-center dynamics that produce Ohmic, Hall and polarization currents on the horizon. A two-block matrix configuration (horizon + environment + bifundamental links) is introduced; the links become tachyonic in a thin shell outside the fuzzy sphere, condense, and lock the world-volume gauge field b_A to the boundary value a_A of the exterior Maxwell field. The parton current thereby becomes a physical source for the exterior field, replacing the fictitious classical membrane by a dynamical quantum membrane. The resulting boundary condition generalizes the classical ingoing condition and yields explicit frequency- and helicity-dependent reflectivity coefficients R_\pm that could produce black-hole echoes and Kerr-like rotation of linear polarization.

Significance. If the construction holds, it supplies the first concrete microscopic realization of the membrane paradigm within a matrix model of quantum black holes, converting a bookkeeping device into a dynamical system of LLL partons whose transport coefficients are in principle computable. The Berry-monopole origin of the tunneling monopole, the explicit locking mechanism, and the closed-form reflectivity formulas (including Hall-induced chirality and polarization current) are genuine advances that open a possible observational window onto horizon microstructure. The large-N continuum reductions, coherent-state maps, quadratic-link diagonalization and appendices are carried through with care and constitute reusable technical machinery for multi-block matrix models.

major comments (3)
  1. [4.5] Section 4.5 (after Eq. (4.74)): the longitudinal conductivity is obtained from a phenomenological Langevin equation with friction coefficient η ~ T^{2}. The classical membrane value σ_xx = 1/4π is recovered only by the additional conjecture c_T = 1/(2q^{2}). Without a first-principles evaluation of the Kubo correlator that fixes c_T, the model does not derive the universal classical conductivity that the membrane paradigm requires; the matching remains an input rather than an output.
  2. [6.3] Section 6.3: the reflective boundary condition (6.69)–(6.76) and the subsequent Kerr-rotation/ellipticity predictions are written under the explicit assumption that the exterior geometry is Schwarzschild. The paper states that this metric has not been derived from the matrix model. The transport coefficients themselves are model-internal, but the conversion into null-coordinate reflectivity and echo phenomenology is not; either a derivation of the metric (or an effective tortoise coordinate) must be supplied, or the geometric step must be cleanly separated from the matrix-model results.
  3. [6.2] After Eq. (6.62): locking is controlled by the stiffness K ~ N^{3} l_P/a_0. While the paper correctly notes that ω, |p| ≪ √N/l_P allows the kinetic terms to be dropped, the reflectivity formulas are later applied at frequencies of order the Hawking scale ~1/R. A quantitative residual-unlocking estimate δb ~ (ω^{2} R^{2}/K)a (including back-reaction of the parton current on the gap) should be given to confirm that the identification j_tot[a] remains under control at those frequencies.
minor comments (4)
  1. The free parameters a0, a2, ν3 and the stretched-horizon proper distance ℓ appear in several normalizations; a short table collecting their values (or the matching conditions that fix them) would improve readability.
  2. [3] Notation for the two time coordinates (t, aũ, au) and the two radii (R, L) is dense; a one-line glossary early in Sec. 3 would help.
  3. Typos: “F uzzy” in several section headings; “back hole” (p. 21); missing space before citations in a few places.
  4. [1] The claim that the same a0 = π/3 is fixed by both Kerr angular momentum and the tunneling rate is important; a brief cross-reference to the precise equations in [4,5] would make the consistency check self-contained.

Circularity Check

2 steps flagged

Classical membrane conductivity 1/4π is recovered only by conjecturing the free Langevin friction c_T; a0 and the black-hole identification are imported from prior self-matched papers, while the locking/LLL/Hall derivations themselves are independent.

specific steps
  1. fitted input called prediction [Sec. 4.5 after Eq. (4.74); reused in Eq. (6.66)]
    "We conjecture that this results in c_T = 1/(2q²) and so the membrane-paradigm value of 1/4π is recovered. ... σ_xx = 1/4π , D:= l_P/(2π a0) , σ_H = qQ/(2π N)."

    The longitudinal conductivity is σ_xx ≃ q² c_T / 2π with c_T a free phenomenological friction parameter. Setting c_T = 1/(2q²) forces σ_xx = 1/4π by construction; the classical membrane value is therefore not a prediction of the LLL dynamics but an input choice. The final boundary condition (6.64)–(6.66) then presents this fitted value as the microscopic Ohmic response.

  2. self citation load bearing [Introduction Eq. (1.3); Abstract; Sec. 4.1]
    "the semi-classical decay rate of a black hole [6] is reproduced provided the condition a0 = π/3 is satisfied. This provides a nontrivial check of the model, since the same condition has previously been obtained from matching the angular momentum of the quantum rotating fuzzy sphere configuration with that of the Kerr black hole. ... It was proposed that a quantum black hole is described by a fuzzy sphere together with a half-filled Fermi sea of horizon partons."

    The dimensionless coefficient a0 that normalizes the continuum gauge coupling, the FIDO time rescaling, and the polarization susceptibility D is fixed by prior self-matching to Kerr angular momentum and to the Page decay rate. The black-hole identification itself (fuzzy sphere + half-filled Fermi sea = horizon) is likewise taken from the author’s earlier papers [1,4,5] that already tuned the same model to macroscopic BH charges and entropy. Those inputs are load-bearing for the present membrane construction and are not independently re-established here.

full rationale

The paper’s central dynamical claims—Berry monopole from fuzzy-sphere topology, LLL projection of fundamental partons, guiding-center Hall response, tachyonic link condensation, and the locking potential V_int ~ K(b−a)² with K ~ N³—are derived within the present calculation and do not reduce by construction to their targets. Circularity is limited and partial: (i) the universal Ohmic value σ_xx = 1/4π that the classical membrane paradigm requires is not computed from the matrix model; it is imposed by conjecturing the free friction coefficient c_T = 1/(2q²) after a phenomenological Langevin treatment; (ii) the model coefficient a0 = π/3 and the identification of the fuzzy-sphere + half-filled Fermi sea with a black-hole horizon are load-bearing inputs taken from the author’s prior matching papers [1,4,5] rather than re-derived here. These steps raise the score above a pure non-finding but do not collapse the locking or Hall/polarization results, so the overall circularity remains moderate (score 4).

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 4 invented entities

The central claim rests on the author's prior matrix model (not standard consensus), large-N continuum maps, a phenomenological friction that is tuned to recover classical conductivity, and the undemonstrated emergence of Schwarzschild geometry. Free parameters and invented entities below list what is not paid for by external benchmarks.

free parameters (5)
  • a0 (kinetic normalization) = π/3
    Fixed to π/3 by matching Kerr angular momentum and tunneling decay rate in prior papers; enters continuum gauge couplings and FIDO time rescaling.
  • a2 (Yukawa coefficient)
    Sets parton charge q = a2/(2a0) and chemical potential scale; not fixed by an independent external measurement in this paper.
  • c_T (dimensionless friction) = 1/(2q²) (conjectured)
    Langevin friction parameter; conjectured equal to 1/(2q²) so that σ_xx recovers the classical membrane value 1/4π.
  • ν3 (environmental volume factor) = 24
    Chosen as 24 to obtain Gauss-unit Maxwell action in the environmental block.
  • stretched-horizon proper distance ℓ = ~ ℓ_P
    Taken ~ ℓ_P to set FIDO time scaling τ ~ t/N; order-1 coefficient is free and affects relative term coefficients only at N-independent level.
axioms (6)
  • ad hoc to paper The matrix quantum mechanics (1.1) with fundamental fermions and negative mass term correctly describes quantum black holes (fuzzy sphere + half-filled Fermi sea).
    Imported from the author's prior proposal [1]; not a standard domain result of string theory or GR.
  • domain assumption Large-N continuum limit converts matrix traces and commutators into continuum integrals and covariant derivatives on S²_R and flat R³.
    Standard fuzzy-sphere / matrix-model lore; used throughout Secs. 3–6 and Appendices A–B.
  • ad hoc to paper Horizon acts as a thermal bath with friction η ~ T² so that a first-order Langevin equation describes parton drift.
    Motivated by correlator decay ~1/R but KMS condition not verified (Sec. 4.5).
  • ad hoc to paper General covariance emerges from the matrix model so that the exterior geometry is Schwarzschild.
    Explicitly assumed without derivation in Sec. 6.3 for the reflective BC analysis.
  • domain assumption Gauss-law constraint of the covariantized multi-block theory identifies net parton charge with asymptotic black-hole charge.
    Standard gauge-theory Gauss law applied to the two-block system (Sec. 5.3).
  • standard math SU(2) coherent-state Berry connection on the fuzzy sphere is a monopole of charge J = (N−1)/2 felt by fundamental (not adjoint) states.
    Standard coherent-state geometry; derived in Appendix C.
invented entities (4)
  • Horizon partons (u and d LLL oscillators) no independent evidence
    purpose: Microscopic charged degrees of freedom that count Bekenstein-Hawking entropy and carry membrane currents.
    Identified with fermionic oscillators of the matrix model; independent evidence limited to entropy matching and proposed charge identification within the same model.
  • Berry monopole intrinsic to the fuzzy sphere no independent evidence
    purpose: Provides LLL structure for partons and microscopic origin of the monopole in tunneling decay.
    Mathematically derived from coherent-state topology; physical role as parent of tunneling monopole is model-specific.
  • Bifundamental link condensate locking b_A to a_A no independent evidence
    purpose: Converts worldvolume parton current into a physical boundary source for exterior Maxwell theory.
    Derived from tachyonic mass of off-diagonal modes in the two-block potential; no external experimental handle.
  • Quantum membrane (dynamical stretched horizon of LLL partons) no independent evidence
    purpose: Replace the fictitious classical membrane with a physical quantum surface.
    Composite of the above; falsifiable only through predicted reflectivity/echoes if the parent model is accepted.

pith-pipeline@v1.1.0-grok45 · 39439 in / 4277 out tokens · 48277 ms · 2026-07-14T10:48:21.533875+00:00 · methodology

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read the original abstract

We develop a microscopic quantum membrane paradigm from the matrix quantum mechanics of black holes [1]. It was proposed that a quantum black hole is described by a fuzzy sphere together with a half-filled Fermi sea of horizon partons. We show that the topology of the fuzzy sphere induces a Berry monopole, providing a microscopic origin for the monopole appearing in the tunneling description of the decay of quantum black hole. Because the partons couple to the fuzzy sphere as fundamental degrees of freedom, they are sensitive to this monopole and form Lowest-Landau-Level (LLL) states rather than ordinary propagating two-dimensional fermions. Their guiding-center dynamics generates Ohmic, Hall, and polarization currents on the horizon. To couple these currents to an external electromagnetic field, we introduce a two-block matrix configuration comprising black-hole, environmental, and bifundamental link sectors. Off-diagonal link modes become tachyonic near the fuzzy sphere and condense, dynamically locking the horizon gauge field to the boundary value of the external Maxwell field. The parton current thereby becomes a physical boundary source for the exterior field. Our construction replaces the fictitious membrane of the classical paradigm with a dynamical quantum membrane populated by microscopic LLL degrees of freedom. The resulting boundary condition generalizes the classical ingoing membrane condition and yields explicit quantum, frequency-dependent, and helicity-dependent corrections, offering a possible probe of the microscopic quantum structure of the horizon.

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Reference graph

Works this paper leans on

45 extracted references · 36 linked inside Pith

  1. [1]

    A Matrix Model Proposal for Quantum Gravity and the Quantum Mechanics of Black Holes,

    C.-S. Chu, “A Matrix Model Proposal for Quantum Gravity and the Quantum Mechanics of Black Holes,”arXiv:2406.01466 [hep-th]. 49

    Pith/arXiv arXiv

  2. [2]

    M theory as a matrix model: A Conjecture,

    T. Banks, W. Fischler, S. H. Shenker, and L. Susskind, “M theory as a matrix model: A Conjecture,”Phys. Rev. D55(1997) 5112–5128,arXiv:hep-th/9610043

    Pith/arXiv arXiv 1997

  3. [3]

    A Large N reduced model as superstring,

    N. Ishibashi, H. Kawai, Y. Kitazawa, and A. Tsuchiya, “A Large N reduced model as superstring,”Nucl. Phys. B498(1997) 467–491,arXiv:hep-th/9612115

    Pith/arXiv arXiv 1997

  4. [4]

    Quantum Kerr black hole from matrix theory of quantum gravity,

    C.-S. Chu, “Quantum Kerr black hole from matrix theory of quantum gravity,”Phys. Rev. D 112no. 4, (2025) 046014,arXiv:2406.12704 [hep-th]

    Pith/arXiv arXiv 2025

  5. [5]

    Hawking Radiation from Tunneling in Black Hole Quantum Mechanics,

    C.-S. Chu, “Hawking Radiation from Tunneling in Black Hole Quantum Mechanics,” arXiv:2603.12199 [hep-th]

    arXiv

  6. [6]

    Particle Emission Rates from a Black Hole: Massless Particles from an Uncharged, Nonrotating Hole,

    D. N. Page, “Particle Emission Rates from a Black Hole: Massless Particles from an Uncharged, Nonrotating Hole,”Phys. Rev. D13(1976) 198–206

    1976

  7. [7]

    Some speculations about black hole entropy in string theory,

    L. Susskind, “Some speculations about black hole entropy in string theory,” arXiv:hep-th/9309145

    Pith/arXiv arXiv

  8. [8]

    M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory,

    W. Taylor, “M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory,”Rev. Mod. Phys.73(2001) 419–462,arXiv:hep-th/0101126

    Pith/arXiv arXiv 2001

  9. [9]

    D-brane field theory on compact spaces,

    W. Taylor, “D-brane field theory on compact spaces,”Phys. Lett. B394(1997) 283–287, arXiv:hep-th/9611042

    Pith/arXiv arXiv 1997

  10. [10]

    Black Hole Eddy Currents,

    T. Damour, “Black Hole Eddy Currents,”Phys. Rev. D18(1978) 3598–3604

    1978

  11. [11]

    Black-hole electrodynamics - an absolute-space/universal-time formulation,

    D. MacDonald and K. S. Thorne, “Black-hole electrodynamics - an absolute-space/universal-time formulation,”Mon. Not. Roy. Astron. Soc.198(1982) 345–383

    1982

  12. [12]

    Membrane Viewpoint on Black Holes: Properties and Evolution of the Stretched Horizon,

    R. H. Price and K. S. Thorne, “Membrane Viewpoint on Black Holes: Properties and Evolution of the Stretched Horizon,”Phys. Rev. D33(1986) 915–941

    1986

  13. [13]

    K. S. Thorne, R. H. Price, and D. A. Macdonald, eds.,BLACK HOLES: THE MEMBRANE PARADIGM. Yale University Press, 1986

    1986

  14. [14]

    An Action for black hole membranes,

    M. Parikh and F. Wilczek, “An Action for black hole membranes,”Phys. Rev. D58(1998) 064011,arXiv:gr-qc/9712077

    Pith/arXiv arXiv 1998

  15. [15]

    Anti de Sitter space and holography,

    E. Witten, “Anti de Sitter space and holography,”Adv. Theor. Math. Phys.2(1998) 253–291, arXiv:hep-th/9802150

    Pith/arXiv arXiv 1998

  16. [16]

    Gauge theory correlators from noncritical string theory,

    S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, “Gauge theory correlators from noncritical string theory,”Phys. Lett. B428(1998) 105–114,arXiv:hep-th/9802109

    Pith/arXiv arXiv 1998

  17. [17]

    The World as a hologram,

    L. Susskind, “The World as a hologram,”J. Math. Phys.36(1995) 6377–6396, arXiv:hep-th/9409089

    Pith/arXiv arXiv 1995

  18. [18]

    Noncommutative open string and D-brane,

    C.-S. Chu and P.-M. Ho, “Noncommutative open string and D-brane,”Nucl. Phys. B550 (1999) 151–168,arXiv:hep-th/9812219. 50

    Pith/arXiv arXiv 1999

  19. [19]

    To gauge or not to gauge?,

    J. Maldacena and A. Milekhin, “To gauge or not to gauge?,”JHEP04(2018) 084, arXiv:1802.00428 [hep-th]

    Pith/arXiv arXiv 2018

  20. [20]

    Black hole spectroscopy: from theory to experiment,

    E. Bertiet al., “Black hole spectroscopy: from theory to experiment,”Class. Quant. Grav.43 no. 12, (2026) 123001,arXiv:2505.23895 [gr-qc]

    Pith/arXiv arXiv 2026

  21. [21]

    Is the gravitational-wave ringdown a probe of the event horizon?,

    V. Cardoso, E. Franzin, and P. Pani, “Is the gravitational-wave ringdown a probe of the event horizon?,”Phys. Rev. Lett.116no. 17, (2016) 171101,arXiv:1602.07309 [gr-qc]. [Erratum: Phys.Rev.Lett. 117, 089902 (2016)]

    Pith/arXiv arXiv 2016

  22. [22]

    Testing the black hole ‘no-hair’ hypothesis,

    V. Cardoso and L. Gualtieri, “Testing the black hole ‘no-hair’ hypothesis,”Class. Quant. Grav.33no. 17, (2016) 174001,arXiv:1607.03133 [gr-qc]

    Pith/arXiv arXiv 2016

  23. [23]

    Echoes from the Abyss: Tentative evidence for Planck-scale structure at black hole horizons,

    J. Abedi, H. Dykaar, and N. Afshordi, “Echoes from the Abyss: Tentative evidence for Planck-scale structure at black hole horizons,”Phys. Rev. D96no. 8, (2017) 082004, arXiv:1612.00266 [gr-qc]

    Pith/arXiv arXiv 2017

  24. [24]

    Tests for the existence of black holes through gravitational wave echoes,

    V. Cardoso and P. Pani, “Tests for the existence of black holes through gravitational wave echoes,”Nature Astron.1no. 9, (2017) 586–591,arXiv:1709.01525 [gr-qc]

    Pith/arXiv arXiv 2017

  25. [25]

    Testing black hole candidates with electromagnetic radiation,

    C. Bambi, “Testing black hole candidates with electromagnetic radiation,”Rev. Mod. Phys. 89no. 2, (2017) 025001,arXiv:1509.03884 [gr-qc]

    Pith/arXiv arXiv 2017

  26. [26]

    Gravitational wave echoes through new windows,

    R. S. Conklin, B. Holdom, and J. Ren, “Gravitational wave echoes through new windows,” Phys. Rev. D98no. 4, (2018) 044021,arXiv:1712.06517 [gr-qc]

    Pith/arXiv arXiv 2018

  27. [27]

    Echoes from Quantum Black Holes,

    Q. Wang, N. Oshita, and N. Afshordi, “Echoes from Quantum Black Holes,”Phys. Rev. D 101no. 2, (2020) 024031,arXiv:1905.00446 [gr-qc]

    Pith/arXiv arXiv 2020

  28. [28]

    Comments on:

    G. Ashton, O. Birnholtz, M. Cabero, C. Capano, T. Dent, B. Krishnan, G. D. Meadors, A. B. Nielsen, A. Nitz, and J. Westerweck, “Comments on: ”Echoes from the abyss: Evidence for Planck-scale structure at black hole horizons”,”arXiv:1612.05625 [gr-qc]

    Pith/arXiv arXiv

  29. [29]

    Low significance of evidence for black hole echoes in gravitational wave data,

    J. Westerweck, A. Nielsen, O. Fischer-Birnholtz, M. Cabero, C. Capano, T. Dent, B. Krishnan, G. Meadors, and A. H. Nitz, “Low significance of evidence for black hole echoes in gravitational wave data,”Phys. Rev. D97no. 12, (2018) 124037,arXiv:1712.09966 [gr-qc]

    Pith/arXiv arXiv 2018

  30. [30]

    Fuzzy Black Holes from Mass Generation in Matrix Compactification,

    D. Laurenzano and J. F. Wheater, “Fuzzy Black Holes from Mass Generation in Matrix Compactification,”arXiv:2511.10430 [hep-th]

    Pith/arXiv arXiv

  31. [31]

    General Relativity in IIB matrix model,

    P.-M. Ho, H. Kawai, and H. C. Steinacker, “General Relativity in IIB matrix model,”JHEP 02(2026) 070,arXiv:2509.06646 [hep-th]

    arXiv 2026

  32. [32]

    The Fuzzball proposal for black holes: An Elementary review,

    S. D. Mathur, “The Fuzzball proposal for black holes: An Elementary review,”Fortsch. Phys. 53(2005) 793–827,arXiv:hep-th/0502050

    Pith/arXiv arXiv 2005

  33. [33]

    Charge currents, rare decays, and black holes,

    E. J. Martinec, “Charge currents, rare decays, and black holes,”arXiv:2303.17139 [hep-th]. 51

    Pith/arXiv arXiv

  34. [34]

    Hawking radiation as tunneling,

    M. K. Parikh and F. Wilczek, “Hawking radiation as tunneling,”Phys. Rev. Lett.85(2000) 5042–5045,arXiv:hep-th/9907001

    Pith/arXiv arXiv 2000

  35. [35]

    Computational Complexity and Black Hole Horizons,

    L. Susskind, “Computational Complexity and Black Hole Horizons,”Fortsch. Phys.64(2016) 24–43,arXiv:1403.5695 [hep-th]. [Addendum: Fortsch.Phys. 64, 44–48 (2016)]

    Pith/arXiv arXiv 2016

  36. [36]

    Black holes and the butterfly effect,

    S. H. Shenker and D. Stanford, “Black holes and the butterfly effect,”JHEP03(2014) 067, arXiv:1306.0622 [hep-th]

    Pith/arXiv arXiv 2014

  37. [37]

    A bound on chaos,

    J. Maldacena, S. H. Shenker, and D. Stanford, “A bound on chaos,”JHEP08(2016) 106, arXiv:1503.01409 [hep-th]

    Pith/arXiv arXiv 2016

  38. [38]

    Remarks on the Sachdev-Ye-Kitaev model,

    J. Maldacena and D. Stanford, “Remarks on the Sachdev-Ye-Kitaev model,”Phys. Rev. D94 no. 10, (2016) 106002,arXiv:1604.07818 [hep-th]

    Pith/arXiv arXiv 2016

  39. [39]

    Dynamics and level statistics of interacting fermions in the lowest landau level,

    M. Fremling, C. Repellin, J.-M. Stéphan, N. Moran, J. K. Slingerland, and M. Haque, “Dynamics and level statistics of interacting fermions in the lowest landau level,”New Journal of Physics20no. 10, (2018) 103036

    2018

  40. [40]

    Cosmological horizons as new examples of membrane paradigm,

    T. Wang, “Cosmological horizons as new examples of membrane paradigm,”Class. Quant. Grav.32no. 19, (2015) 195006,arXiv:1411.6445 [gr-qc]

    Pith/arXiv arXiv 2015

  41. [41]

    Cosmological Collider Physics,

    N. Arkani-Hamed and J. Maldacena, “Cosmological Collider Physics,”arXiv:1503.08043 [hep-th]

    Pith/arXiv arXiv

  42. [42]

    The Construction on noncommutative manifolds using coherent states,

    H. Grosse and P. Presnajder, “The Construction on noncommutative manifolds using coherent states,”Lett. Math. Phys.28(1993) 239–250

    1993

  43. [43]

    The Origin of chiral anomaly and the noncommutative geometry,

    P. Presnajder, “The Origin of chiral anomaly and the noncommutative geometry,”J. Math. Phys.41(2000) 2789–2804,arXiv:hep-th/9912050

    Pith/arXiv arXiv 2000

  44. [44]

    Towards finite quantum field theory in noncommutative geometry,

    H. Grosse, C. Klimcik, and P. Presnajder, “Towards finite quantum field theory in noncommutative geometry,”Int. J. Theor. Phys.35(1996) 231–244,arXiv:hep-th/9505175

    Pith/arXiv arXiv 1996

  45. [45]

    Scaling limits of the fuzzy sphere at one loop,

    C.-S. Chu, J. Madore, and H. Steinacker, “Scaling limits of the fuzzy sphere at one loop,” JHEP08(2001) 038,arXiv:hep-th/0106205. 52

    Pith/arXiv arXiv 2001