Pith. sign in

REVIEW 2 major objections 6 minor 73 references

The leading-soft cubic graviton self-interaction on the black-hole horizon

T0 review · 2 major / 6 minor · reviewed 2026-08-01 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper proves a vanishing theorem: at leading soft order, the self-coupling of traceless longitudinal gravitons on the Schwarzschild horizon is identically zero, and the surviving trace-sector vertex cannot thermalize the sector.

desk verdict A careful, transparent derivation of the GGV cubic self-interaction; the vanishing theorem is exact only in the rigid-sphere limit, where the corrections are as large as the survivor. read the letter →

arxiv 2607.21066 v1 pith:QEHYS4PH submitted 2026-07-23 gr-qc hep-thquant-ph

Ayanendu Dutta This is my paper
classification gr-qchep-thquant-ph MSC 83C5783C4583C47 PACS 04.70.-s04.60.-m03.67.-a
keywords gravitonself-interactionblack-holehorizonnear-horizonframeworkRegge-WheelergaugesoftlimitEulerdensityquantumsimulationperturbativerigidity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

At leading order in the soft (low-momentum) expansion around a Schwarzschild horizon, the graviton's cubic self-interaction is almost entirely suppressed: the self-coupling among purely traceless longitudinal polarizations is exactly zero, because in the near-horizon two-dimensional block the Einstein–Hilbert action collapses to a total (Euler) derivative at every order in κ. The only surviving self-interaction runs through the trace/transverse-scalar sector, with a closed-form on-shell weight W(λ,λ,λ) = −3λ(2λ²+λ+3)/(λ+1)². Combined with a provably resonance-free boost spectrum (minimal cubic mismatch 0.565/R_S, asymptotically 1/2), this analytic structure predicts that the longitudinal sector is perturbatively rigid — the cubic vertex alone cannot thermalize or scramble the horizon. The paper's quantum simulations confirm this quantitatively: a dressed single eigenstate (d_eff = 1.06), an inelasticity η ≈ 0.12, and entanglement 2.3 nats below Haar. The result matters because it narrows the mechanism space for Page-like behavior in the near-horizon framework: the hhh vertex is not what thermalizes the horizon.

What carries the argument

Two pieces carry the argument. (1) The warped-product identity √−g R = √−g^(2) [Ω²R^(2) + 2(∇Ω)²] − 4 ∂_a(√−g^(2) Ω g^(2)ab ∂_b Ω): when the transverse-sphere fluctuation K (and hence the warp factor Ω = 1+κK) is set to zero, the four-dimensional scalar curvature collapses exactly to the two-dimensional Ricci scalar √−g^(2) R^(2), which in two dimensions is the Euler density and therefore a total derivative at every order in κ — the geometric mechanism of Theorem 1. (2) The near-horizon boost spectrum ω_ℓ = √(ℓ²+ℓ+1)/R_S, which is provably resonance-free for cubic processes (every allowed triad has |ω_3 − ω_1 − ω_2| ≥ 0.565/R_S, tending to 1/2), so every retained b†b†b vertex acts off shell

What would settle it

Compute the cubic Einstein–Hilbert vertex onto traceless longitudinal polarizations in the same gauge but retaining the O(µ²) transverse-curvature terms (or with K ≠ 0 at leading soft order). If the traceless self-coupling reappears at order µ² with a coefficient that is not suppressed relative to the trace-sector survivor, the vanishing theorem's physical extension fails; equivalently, a gauge-invariant computation of the on-shell three-graviton amplitude on the Schwarzschild background that yields a nonzero traceless projection at leading soft order would falsify the framework-specific claim

Watch

Extended reading notes

Core claim

Expanding the Einstein–Hilbert action to cubic order about the Schwarzschild horizon in the even Regge–Wheeler gauge of the near-horizon framework, the paper proves a vanishing theorem: with the transverse-scalar/trace sector switched off, the metric fluctuation becomes a two-dimensional block whose √−g R is a total (Euler) derivative at every order in κ, so the on-shell cubic self-coupling of the traceless longitudinal polarizations is identically zero. The surviving interaction lives entirely in the trace sector, and its on-shell equal-ℓ weight is the closed-form W(λ,λ,λ) = −3λ(2λ²+λ+3)/(λ+1)² (W(7,7,7) = −35.4375), reproduced by two independent derivations. The same structural facts — the

Load-bearing premise

The result depends on the leading-soft truncation in which the transverse sphere is held rigid (transverse-scalar fluctuation K = 0 and finite curvature µ² = 1/R² dropped); if these neglected contributions are not negligible at leading order on the real horizon, the vanishing of the traceless self-coupling does not extend beyond the strict µ → 0 limit, and the paper itself quantifies ~20% soft/scheme systematics at the only simulable multiplet ℓ = 2.

Editorial extensions

If this is right

  • If Theorem 1 holds, the leading-soft cubic graviton vertex on the horizon has no traceless self-coupling; all number-changing self-interaction is carried by the trace/transverse-scalar sector with the closed-form weight W.
  • The hhh vertex by itself cannot thermalize or scramble the longitudinal sector; Page-like behavior in the near-horizon framework must come from the exchange/eikonal sector or from beyond-leading-soft kernels.
  • The resonance-free spectrum (gap → 1/2) makes every cubic process off shell, so the cubic interaction acts as a dressing rather than a delocalizer — quantitatively measured as d_eff = 1.06 and η ≈ 0.12 at ℓ = 2.
  • The cubic vertex alone opens the inelastic channel ϕϕ→hh→4ϕ, with pre-registered fourth-order power laws (exponents 2.000, 6.000, 7.92) confirmed by simulation.
  • All simulation results agree with exact diagonalization; the reported numbers carry stated systematics, including a ~20% soft/scheme uncertainty on the vertex at ℓ = 2.

Reading between the lines

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

  • The Euler-derivative mechanism is geometric and gauge/scheme-specific: if it survives relaxation of the rigid-sphere assumption (finite µ²) at higher ℓ or in a different gauge, it would point to a general softness of longitudinal horizon gravitons; if not, the theorem is an artifact of the near-horizon truncation. The paper explicitly flags ~20% corrections at ℓ = 2, so the honest extension is tha
  • A decisive test of the physical claim would be to compute the cubic vertex projecting on traceless longitudinal polarizations with the O(µ²) terms retained; a nonzero leading-order result would falsify the extension, while a suppressed (but nonzero) result would still preserve the qualitative rigidity.
  • The low measured entanglement (2.3 nats below Haar) suggests the sector is amenable to tensor-network methods at much larger registers; the paper's own scaling analysis implies that the rigidity/chaos question can be settled classically before quantum hardware is needed, and hardware becomes interesting only where entanglement grows toward the Page value.
  • The 'noise manufactures inelasticity' result — depolarizing noise creates spurious η up to 0.95 — is a transferable protocol lesson: any near-term hardware claim of gravitational particle production must be reported jointly with fidelity and symmetry-violation fractions.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 6 minor

Summary. The paper expands the Einstein–Hilbert action to cubic order about the Schwarzschild horizon in the even Regge–Wheeler gauge of the GGV near-horizon framework, and derives an effective cubic graviton self-interaction vertex. The central formal result is a “vanishing theorem”: in the strict soft limit in which the transverse sphere is held rigid (µ→0, K=0), the cubic self-coupling of the traceless longitudinal polarizations vanishes identically because the two-dimensional longitudinal block of √−g R is a total (Euler) derivative at every order in κ. The surviving interaction is carried by the trace/transverse-scalar sector, with a closed-form on-shell equal-λ weight W(λ,λ,λ)=−3λ(2λ²+λ+3)/(λ+1)². The paper then second-quantizes this vertex, assembles a full near-horizon Hamiltonian, and studies its real-time dynamics on IBM Qiskit/Aer with extensive cross-validation against exact diagonalization. The simulation finds perturbative rigidity (d_eff=1.06, inelasticity η≈0.12, sub-Haar entanglement), which the authors emphasize is analytically predicted by a resonance-free boost spectrum and bounded vertex magnitudes, not independently discovered by the simulation. All major modeling choices and the ~20% soft/scheme systematc at the only simulable multiplet ℓ=2 are explicitly declared.

Significance. If the result holds, the paper makes a sharp and useful contribution to the near-horizon S-matrix program: it provides the first explicit, first-principles cubic graviton self-interaction vertex in the GGV reduction, with no free O(1) contraction constant, and it demonstrates that the leading-soft self-interaction is structurally incapable of thermalizing or scrambling the longitudinal sector by itself. The derivation is supported by multiple independent engines, including exact nonlinear GR evaluation and an independent dilaton-form reduction, and the simulation pipeline is unusually transparent: machine-checked operator identities, decomposition-independence checks, validated Trotter scaling, and explicit noise budgets. The paper also introduces a symmetry-preserving total-occupation truncation that is exactly su(2)-invariant, which is a methodological improvement. The central limitation is equally clear: the vanishing theorem and the closed-form weight are statements about a strict two-dimensional, rigid-sphere limit, and the paper itself quantifies 10–21% corrections at ℓ=2, plus large prescription dependence of the off-diagonal multi-ℓ weights. The honesty and reproducibility

major comments (2)
  1. [Sec. IV C / Remark 2 / Modeling choice 1] The physical interpretation of the headline result is governed by the rigid-sphere, µ→0 approximation. The paper explicitly states that restoring finite transverse curvature reintroduces O(µ²) traceless-sector couplings at ~14% of the trace-sector survivor at ℓ=2, that retaining the exact trace amplitude shifts W by ~10%, and that the off-shell prescription changes W by ~21%. These are not small compared with the surviving trace vertex. Because the Hamiltonian of Eq. (24)–(25) is built from the trace-only vertex and then simulated, the quantitative results (η≈0.12, d_eff=1.06, TV values) are not yet predictions for the finite-R physical horizon. The paper is transparent about this, but the abstract and conclusion still present the trace-channel vertex as “the leading self-interaction” without the strict-limit qualifier. Please either compute or bound the O(µ²) traceless cubic couplings i
  2. [Sec. III C / Appendix B] The claimed flat-space limit gate is asserted but not demonstrated. The paper states that the derived vertex reduces to the known DeWitt/Sannan three-graviton vertex ‘by construction,’ but no explicit comparison is shown. Since the three independent derivation engines share the same metric ansatz, gauge choice, and GGV polarization data, an external anchor against the known flat-space h(∂h)² three-graviton amplitude would materially strengthen the result. Please provide the explicit µ→0 limit of the derived on-shell weight and vertex table and compare it with the known flat-space three-graviton vertex; if the comparison cannot be made in this gauge, state the obstruction explicitly.
minor comments (6)
  1. [Abstract] The phrase “the leading self-interaction lives entirely in the trace channel” should carry the qualifier “in the strict µ→0 soft limit” in the abstract itself, not only in Remark 2, to avoid an unqualified physical reading.
  2. [Sec. VII] The kernel K(p1,p2,p3) is introduced in Eq. (17) but defined only later in Eq. (23). A one-sentence pointer at first use would improve readability.
  3. [Sec. X F] The fitted exponent 7.92 for P4∝t^8 is quoted without the fit window. Please state the time interval used for the log–log fit and the estimated fit uncertainty.
  4. [Sec. II] The factor-2 normalization difference with the GGV toolbox is mentioned but not displayed. A short equation showing the field normalization that maps the toolbox’s −1/2 quadratic coefficient to the −1/4 used here would prevent reader confusion.
  5. [Sec. IV C] In the sentence following Eq. (16), “large-λ behaviour W→−6λ+9−21/λ” is stated without derivation; a one-line expansion would help. Also, the symbol δ_S2 for the transverse sphere metric is potentially confusing, since δ_AB usually denotes a Kronecker delta; please clarify the convention.
  6. [Sec. VIII B(c)] The statement that the closest allowed triad is ℓ3=ℓ1+ℓ2 and smaller ℓ3 only increases the mismatch is plausible but is only checked numerically to ℓ≤16. Please state whether this has been proven analytically for all ℓ or identify it as a numerical audit.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central vertex derivation is self-contained, the simulation is explicitly confirmatory rather than an independent discovery claim, and the framework-specific scope is disclosed.

full rationale

The central derivation is self-contained rather than circular. Theorem 1 follows from an explicit geometric input — the even Regge–Wheeler gauge two-block metric and the rigid-sphere/leading-soft truncation — and from the mathematical fact that a two-dimensional √−g R is a total derivative (Gauss–Bonnet). This is a real derivation, not an input renamed as an output: the vanishing of the traceless longitudinal self-coupling is a consequence of the 2D Euler-density structure, and the paper exhibits the cancellation order by order (Appendix E). The surviving on-shell weight W(7,7,7) = −35.4375 is obtained by contracting the expanded cubic vertex on the GGV residue polarizations and is independently reproduced by a separate dilaton-form derivation (Appendix D1), so it is not fitted from the simulation. The simulation statements are carefully framed as confirmations of analytic structure rather than independent discoveries: the paper says the resonance-free spectrum and the vanishing theorem 'already predict' rigidity and that the simulation 'confirms this quantitatively and measures the residual dressing ... rather than discovering it.' The fourth-order power laws in Sec. X F are explicitly labeled 'perturbative consistency checks' with known exponents, so their confirmation is a validation of the implementation, not a by-construction prediction presented as a discovery. The GGV framework is cited as external prior work by other authors; the argument does not rest on a self-citation chain. The main caveat — that the vanishing theorem holds in the strict μ→0 rigid-sphere limit and does not transfer verbatim to finite R, with ∼10–21% systematics at ℓ=2 — is stated explicitly in Remark 2, Sec. IV C, and Appendix C. That is a disclosed scope limitation, not circularity. The paper is unusually transparent about what is derived, what is confirmed, and what remains scheme-dependent.

Assumptions & free parameters 3 free parameters · 7 assumptions · 0 invented entities

No new particles or forces are invented. All entities (GGV longitudinal graviton, modes, charge Q) are constructions from prior framework or defined within the model. The central derivation relies on stated domain assumptions (GGV reduction, warped product, soft limit) and standard math (Gauss–Bonnet).

free parameters (3)
  • reduced coupling ~g = 12 (representative; swept 0–15)
    The physical coupling γ|W| is Planck-suppressed; simulations sweep the overall scale ~g that multiplies the gravitationally fixed vertex structure. It is a chosen scale parameter, not fitted to data, but the central dynamical results (η=0.12, power laws, d_eff=1.06) depend on it.
  • per-mode occupation cutoff d = 4 (production; 5,6 overlays)
    Bosonic modes truncated at d=4 quanta; results are checked against d=5,6 (max shift |Δη|≤0.0144). A truncation parameter, not fitted, but governs Hilbert-space size.
  • off-shell prescription for multi-ℓ W = Appendix A ordering vs H0–H3 (span factor ~3)
    The equal-ℓ on-shell weight W(λ,λ,λ) is prescription-independent, but the multi-ℓ ratios W(λ_i)/W(7,7,7) depend on the choice of off-shell continuation; the paper reports up to ~70% differences on largest entries between H0 and Appendix A. This is a scheme choice, not fitted, but affects the multi-ℓ results (Δη=-8.6%, TV=0.093).
assumptions (7)
  • domain assumption The Einstein–Hilbert action with minimal coupling is the correct classical starting point.
    Sec. II Eq. (2); the entire derivation expands this action. Standard, but a domain assumption.
  • domain assumption The GGV near-horizon framework: the horizon S-matrix organizes by partial waves with boost frequencies ω_ℓ = sqrt(ℓ²+ℓ+1)/R_S, and the even Regge–Wheeler gauge reduction to a longitudinal tensor and transverse scalar is valid.
    Sec. II, relying on toolbox [5].
  • domain assumption The near-horizon metric can be written as a warped product g(2)⊕(1+κK)δ_{S²} with a rigid transverse sphere at leading soft order.
    Sec. IV A; this makes the 2D topological argument applicable. If K fluctuations are not negligible at leading order, Theorem 1 fails.
  • standard math Gauss–Bonnet theorem: in two dimensions, ∫√-g R is a topological invariant, so its κ-expansion is a total derivative at every order.
    Sec. IV B, Eq. (14), Appendix E.
  • domain assumption Leading-soft truncation: transverse-derivative and O(µ²) background-curvature terms are dropped; the soft limit µ→0 is the regime where the theorem and weight W apply.
    Modeling choice 1, Sec. V; at ℓ=2 corrections are ~14–20%.
  • domain assumption The GGV propagator residue polarizations (P=λ/(λ+1), K=-1, H̄=-2/(λ+1)) correctly define the on-shell projection of the vertex.
    Sec. IV C; used to compute W.
  • domain assumption Second quantization in the GGV in/out vacuum is valid, and the hierarchy truncation retaining ΔN=±1 and dropping ΔN=±3 is justified by the off-shell scale separation.
    Sec. VII and Appendix C9.

how reviews work

0 comments
Cite this review

Pith. "Pith review of The leading-soft cubic graviton self-interaction on the black-hole horizon." pith.science (2026). https://pith.science/paper/QEHYS4PH

@misc{pith2026260721066,
  author       = {Pith},
  title        = {Pith review of: The leading-soft cubic graviton self-interaction on the black-hole horizon},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QEHYS4PH}},
  note         = {Machine review of arXiv:2607.21066}
}
abstract

We expand the Einstein-Hilbert action to cubic order about the Schwarzschild horizon, in the even Regge-Wheeler gauge of the Gaddam-Groenenboom-'t~Hooft (GGV) near-horizon framework, and derive the cubic graviton self-interaction. Our central result is a `vanishing theorem': at leading soft order the self-coupling of the purely traceless longitudinal polarizations is identically zero, because with the trace/transverse-scalar sector switched off the fluctuation reduces to a two-dimensional block whose $\sqrt{-g}\,R$ is a total (Euler) derivative at every order in $\kappa$. We prove this by an explicit closed-form reduction and exhibit the cancellation term by term. It is a `framework-specific' statement, even RW gauge, GGV sector, leading soft order, not a gauge-invariant theorem of general relativity. The theorem is exact, but the quantized vertex inherits a $\sim\!20\%$ soft/scheme systematic at the only simulable multiplet ($\ell=2$), which we state explicitly. We then simulate the real-time dynamics of the resulting Hamiltonian on IBM Qiskit/Aer with exact cross-checks. Two structural facts, a conserved charge that only the cubic vertex violates, opening $\phi\phi\to hh\to4\phi$, and a provably resonance-free boost spectrum (gap $\to1/2$), already predict that the longitudinal channel is perturbatively rigid; the simulation confirms this quantitatively and measures the residual dressing ($d_{\rm eff}=1.06$; multiplicity far from thermal, Poisson, and Haar references) rather than discovering it. A symmetry-exact total-occupation truncation yields the first sector-resolved level statistics, indicative of intermediate behaviour on Hilbert spaces too small to be decisive. All circuit results agree with exact diagonalization, every headline number carries a stated systematic, and hardware execution is deferred behind a quantified noise budget.

Figures

Figures reproduced from arXiv: 2607.21066 by the authors.

Figure 1
Figure 1. FIG. 1. The complete circuit for the smallest instance of [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The sequential-segment snapshot protocol: [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The Hadamard-test interferometer measuring the [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (16 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Multiplicity dynamics [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Inelasticity [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Structure ablation of ¯p [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Late-time ¯p [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Mode-bipartition entanglement profile at several [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. The [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Pre-registered fourth-order power laws of the opened channel, with fitted exponents 2 [PITH_FULL_IMAGE:figures/full_fig_p015_11.png]
Figure 14
Figure 14. Figure 14: FIG. 14. Quadrature squared commutator on the [PITH_FULL_IMAGE:figures/full_fig_p016_14.png]
Figure 13
Figure 13. Figure 13: FIG. 13. Physical fixed-( [PITH_FULL_IMAGE:figures/full_fig_p016_13.png]
Figure 15
Figure 15. Figure 15: FIG. 15. Depolarizing-noise study at fixed depth (29520 cx): fidelity (left) and measured inelasticity (right) versus two-qubit [PITH_FULL_IMAGE:figures/full_fig_p017_15.png]
Figure 16
Figure 16. Figure 16: FIG. 16. Elastic-benchmark Trotter-error calibration: gen [PITH_FULL_IMAGE:figures/full_fig_p023_16.png]
Figure 17
Figure 17. Figure 17: FIG. 17. Inverted-oscillator squared commutator versus the [PITH_FULL_IMAGE:figures/full_fig_p023_17.png]
Figure 18
Figure 18. Figure 18: FIG. 18. Synchronized, oscillatory growth of [PITH_FULL_IMAGE:figures/full_fig_p026_18.png]
Figure 19
Figure 19. Figure 19: FIG. 19. Multi- [PITH_FULL_IMAGE:figures/full_fig_p027_19.png]
Figure 20
Figure 20. Figure 20: FIG. 20. Entanglement profile versus coupling at [PITH_FULL_IMAGE:figures/full_fig_p027_20.png]
Figure 24
Figure 24. Figure 24: FIG. 24. IHO-in-a-box spectrum and spacing statistics ( [PITH_FULL_IMAGE:figures/full_fig_p027_24.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

73 extracted references · 2 linked inside Pith

  1. [68]

    A. Dutta, “The leading-soft cubic graviton self- interaction on the black-hole horizon’,’ github 20 Appendix A: Conventions and the explicit vertex table The derived on-shell weight.The surviving trace-sector vertex of Sec. IV, contracted on the GGV residue po- larizations at rest-frame kinematics (p i ·p j =−ω iωj, ωℓ = √ λ,µ= 1; legs 1,2 creation, leg 3...

  2. [1]

    The Scattering matrix approach for the quantum black hole: An Overview,

    G. ’t Hooft, “The Scattering matrix approach for the quantum black hole: An Overview,” Int. J. Mod. Phys. A11, 4623-4688 (1996)

    1996

  3. [2]

    The Gravitational Shock Wave of a Massless Particle,

    T. Dray and G. ’t Hooft, “The Gravitational Shock Wave of a Massless Particle,” Nucl. Phys. B253, 173-188 (1985)

    1985

  4. [3]

    Quan- tum gravity on the black hole horizon,

    N. Gaddam, N. Groenenboom and G. ’t Hooft, “Quan- tum gravity on the black hole horizon,” JHEP01, 023 (2022)

    2022

  5. [4]

    2→2N scattering: Eikonalisation and the Page curve,

    N. Gaddam and N. Groenenboom, “2→2N scattering: Eikonalisation and the Page curve,” JHEP01, 146 (2022)

    2022

  6. [5]

    A toolbox for black hole scattering,

    N. Gaddam and N. Groenenboom, “A toolbox for black hole scattering,” [arXiv:2207.11277 [hep-th]]

    arXiv

  7. [6]

    Black holes, quantum chaos, and the Riemann hypothesis,

    P. Betzios, N. Gaddam and O. Papadoulaki, “Black holes, quantum chaos, and the Riemann hypothesis,” Sci- Post Phys. Core4, 032 (2021)

    2021

  8. [7]

    Graviton Dominance in Ultrahigh-Energy Scattering,

    G. ’t Hooft, “Graviton Dominance in Ultrahigh-Energy Scattering,” Phys. Lett. B198, 61-63 (1987)

    1987

Show all 73 references
  1. [8]

    Superstring Collisions at Planckian Energies,

    D. Amati, M. Ciafaloni and G. Veneziano, “Superstring Collisions at Planckian Energies,” Phys. Lett. B197, 81 (1987)

    1987

  2. [9]

    Classical and Quantum Gravity Effects from Planckian Energy Super- string Collisions,

    D. Amati, M. Ciafaloni and G. Veneziano, “Classical and Quantum Gravity Effects from Planckian Energy Super- string Collisions,” Int. J. Mod. Phys. A3, 1615-1661 (1988)

    1988

  3. [10]

    Scattering at Planck- ian energies,

    H. L. Verlinde and E. P. Verlinde, “Scattering at Planck- ian energies,” Nucl. Phys. B371, 246-268 (1992)

    1992

  4. [11]

    Eikonal quantum gravity and Planckian scattering,

    D. N. Kabat and M. Ortiz, “Eikonal quantum gravity and Planckian scattering,” Nucl. Phys. B388, 570-592 (1992)

    1992

  5. [12]

    The gravitational eikonal: From parti- cle, string and brane collisions to black-hole encounters,

    P. Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano, “The gravitational eikonal: From parti- cle, string and brane collisions to black-hole encounters,” Phys. Rept.1083, 1-169 (2024)

    2024

  6. [13]

    Black hole S-matrix for a scalar field,

    P. Betzios, N. Gaddam and O. Papadoulaki, “Black hole S-matrix for a scalar field,” JHEP07, 017 (2021)

    2021

  7. [14]

    Charged particle scattering near the horizon,

    F. Feleppa, N. Gaddam and N. Groenenboom, “Charged particle scattering near the horizon,” JHEP02, 148 (2024)

    2024

  8. [15]

    All near-horizon symme- tries of the Schwarzschild black hole in linearised grav- ity,

    A. Aggarwal and N. Gaddam, “All near-horizon symme- tries of the Schwarzschild black hole in linearised grav- ity,” JHEP01, 031 (2025)

    2025

  9. [16]

    Black hole unitarity and antipodal entan- glement,

    G. ’t Hooft, “Black hole unitarity and antipodal entan- glement,” Found. Phys.46, no.9, 1185-1198 (2016)

    2016

  10. [17]

    Eikonal ampli- tudes from curved backgrounds,

    T. Adamo, A. Cristofoli and P. Tourkine, “Eikonal ampli- tudes from curved backgrounds,” SciPost Phys.13, no.2, 032 (2022)

    2022

  11. [18]

    From shock- waves to the gravitational memory effect,

    T. He, A. M. Raclariu and K. M. Zurek, “From shock- waves to the gravitational memory effect,” JHEP01, 006 (2024)

    2024

  12. [19]

    Celestial eikonal amplitudes in the near-horizon region,

    K. Fernandes, F. L. Lin and A. Mitra, “Celestial eikonal amplitudes in the near-horizon region,” Phys. Rev. D 110, no.12, 12 (2024)

    2024

  13. [20]

    Gravitational Regge bounds,

    K. H¨ aring and A. Zhiboedov, “Gravitational Regge bounds,” SciPost Phys.16, no.1, 034 (2024)

    2024

  14. [21]

    Where Is String Theory in the Space of Scattering Amplitudes?,

    A. Guerrieri, J. Penedones and P. Vieira, “Where Is String Theory in the Space of Scattering Amplitudes?,” Phys. Rev. Lett.127, no.8, 081601 (2021)

    2021

  15. [22]

    Where is M-theory in the space of scattering ampli- tudes?,

    A. Guerrieri, H. Murali, J. Penedones and P. Vieira, “Where is M-theory in the space of scattering ampli- tudes?,” JHEP06, 064 (2023)

    2023

  16. [23]

    Chaos in the black hole S-matrix,

    J. Polchinski, “Chaos in the black hole S-matrix,” [arXiv:1505.08108 [hep-th]]

    arXiv

  17. [24]

    Quantum Simulation for High-Energy Physics,

    C. W. Bauer, Z. Davoudi, A. B. Balantekin, T. Bhat- tacharya, M. Carena, W. A. de Jong, P. Draper, A. El- Khadra, N. Gemelke and M. Hanada,et al.“Quantum Simulation for High-Energy Physics,” PRX Quantum4, no.2, 027001 (2023)

    2023

  18. [25]

    Digital Quantum Sim- ulation of Minimal AdS/CFT,

    L. Garc ´ ıa-´Alvarez, I. L. Egusquiza, L. Lamata, A. del Campo, J. Sonner and E. Solano, “Digital Quantum Sim- ulation of Minimal AdS/CFT,” Phys. Rev. Lett.119, 040501 (2017)

    2017

  19. [26]

    Quantum simulation of the non-fermi-liquid state of Sachdev-Ye-Kitaev model,

    Z. Luo, Y. Z. You, J. Li, C. M. Jian, D. Lu, C. Xu, B. Zeng and R. Laflamme, “Quantum simulation of the non-fermi-liquid state of Sachdev-Ye-Kitaev model,” npj Quantum Inf.5, 53 (2019)

    2019

  20. [27]

    Sachdev-Ye-Kitaev model on a noisy quantum com- puter,

    M. Asaduzzaman, R. G. Jha and B. Sambasivam, “Sachdev-Ye-Kitaev model on a noisy quantum com- puter,” Phys. Rev. D109, no.10, 105002 (2024)

    2024

  21. [28]

    Verified Quan- tum Information Scrambling,

    K. A. Landsman, C. Figgatt, T. Schuster, N. M. Linke, B. Yoshida, N. Y. Yao and C. Monroe, “Verified Quan- tum Information Scrambling,” Nature567, no.7746, 61- 65 (2019)

    2019

  22. [29]

    Information scrambling in quantum circuits,

    X. Mi, P. Roushan, C. Quintana, S. Mandra, J. Marshall, C. Neill, F. Arute, K. Arya, J. Atalaya and R. Babbush, et al.“Information scrambling in quantum circuits,” Sci- ence374, no.6574, abg5029 (2021) 19

    2021

  23. [30]

    Traversable wormhole dynamics on a quantum proces- sor,

    D. Jafferis, A. Zlokapa, J. D. Lykken, D. K. Kolch- meyer, S. I. Davis, N. Lauk, H. Neven and M. Spiropulu, “Traversable wormhole dynamics on a quantum proces- sor,” Nature612, no.7938, 51-55 (2022) [erratum: Na- ture640, no.8060, E32 (2025)]

    2022

  24. [31]

    To- ward simulating superstring/M-theory on a quantum computer,

    H. Gharibyan, M. Hanada, M. Honda and J. Liu, “To- ward simulating superstring/M-theory on a quantum computer,” JHEP07, 140 (2021)

    2021

  25. [32]

    Matrix-Model Simula- tions Using Quantum Computing, Deep Learning, and Lattice Monte Carlo,

    E. Rinaldi, X. Han, M. Hassan, Y. Feng, F. Nori, M. McGuigan and M. Hanada, “Matrix-Model Simula- tions Using Quantum Computing, Deep Learning, and Lattice Monte Carlo,” PRX Quantum3, no.1, 010324 (2022)

    2022

  26. [33]

    Observation of quantum Hawking radi- ation and its entanglement in an analogue black hole,

    J. Steinhauer, “Observation of quantum Hawking radi- ation and its entanglement in an analogue black hole,” Nature Phys.12, 959 (2016)

    2016

  27. [34]

    Observation of thermal Hawking radia- tion and its temperature in an analogue black hole,

    J. R. Mu˜ noz de Nova, K. Golubkov, V. I. Kolobov and J. Steinhauer, “Observation of thermal Hawking radia- tion and its temperature in an analogue black hole,” Na- ture569, no.7758, 688-691 (2019)

    2019

  28. [35]

    Quantum Gravity in the Lab. I. Telepor- tation by Size and Traversable Wormholes,

    A. R. Brown, H. Gharibyan, S. Leichenauer, H. W. Lin, S. Nezami, G. Salton, L. Susskind, B. Swingle and M. Walter, “Quantum Gravity in the Lab. I. Telepor- tation by Size and Traversable Wormholes,” PRX Quan- tum4, no.1, 010320 (2023)

    2023

  29. [36]

    Quantum Gravity in the Lab. II. Telepor- tation by Size and Traversable Wormholes,

    S. Nezami, H. W. Lin, A. R. Brown, H. Gharibyan, S. Leichenauer, G. Salton, L. Susskind, B. Swingle and M. Walter, “Quantum Gravity in the Lab. II. Telepor- tation by Size and Traversable Wormholes,” PRX Quan- tum4, no.1, 010321 (2023)

    2023

  30. [37]

    Towards Quantum Gravity in the Lab on Quantum Processors,

    I. Shapoval, V. P. Su, W. de Jong, M. Urbanek and B. Swingle, “Towards Quantum Gravity in the Lab on Quantum Processors,” Quantum7, 1138 (2023)

    2023

  31. [38]

    Quantum Computation vs. Firewalls,

    D. Harlow and P. Hayden, “Quantum Computation vs. Firewalls,” JHEP06, 085 (2013)

    2013

  32. [39]

    Com- putational pseudorandomness, the wormhole growth paradox, and constraints on the AdS/CFT duality,

    A. Bouland, B. Fefferman and U. Vazirani, “Com- putational pseudorandomness, the wormhole growth paradox, and constraints on the AdS/CFT duality,” [arXiv:1910.14646 [quant-ph]]

    1910 arXiv

  33. [40]

    Soft graviton ex- change and the information paradox,

    N. Gaddam and N. Groenenboom, “Soft graviton ex- change and the information paradox,” Phys. Rev. D109, no.2, 026007 (2024)

    2024

  34. [41]

    The Black Hole S-Matrix from Quantum Mechanics,

    P. Betzios, N. Gaddam and O. Papadoulaki, “The Black Hole S-Matrix from Quantum Mechanics,” JHEP11, 131 (2016)

    2016

  35. [42]

    Simulating physics with computers,

    R. P. Feynman, “Simulating physics with computers,” Int. J. Theor. Phys.21, 467-488 (1982)

    1982

  36. [43]

    Universal Quantum Simulators,

    S. Lloyd, “Universal Quantum Simulators,” Science273, no.5278, 1073 (1996)

    1996

  37. [44]

    Quantum Algorithms for Quantum Field Theories,

    S. P. Jordan, K. S. M. Lee and J. Preskill, “Quantum Algorithms for Quantum Field Theories,” Science336, 1130-1133 (2012)

    2012

  38. [45]

    Gravitational perturbations of the Schwarzschild spacetime: A Practical covariant and gauge-invariant formalism,

    K. Martel and E. Poisson, “Gravitational perturbations of the Schwarzschild spacetime: A Practical covariant and gauge-invariant formalism,” Phys. Rev. D71, 104003 (2005)

    2005

  39. [46]

    Stability of a Schwarzschild singularity,

    T. Regge and J. A. Wheeler, “Stability of a Schwarzschild singularity,” Phys. Rev.108, 1063-1069 (1957)

    1957

  40. [47]

    Effective potential for even parity Regge- Wheeler gravitational perturbation equations,

    F. J. Zerilli, “Effective potential for even parity Regge- Wheeler gravitational perturbation equations,” Phys. Rev. Lett.24, 737-738 (1970)

    1970

  41. [48]

    Quantization of gravity in the black hole background,

    R. Kallosh and A. A. Rahman, “Quantization of gravity in the black hole background,” Phys. Rev. D104, no.8, 086008 (2021)

    2021

  42. [49]

    Quantum Theory of Gravity. 2. The Man- ifestly Covariant Theory,

    B. S. DeWitt, “Quantum Theory of Gravity. 2. The Man- ifestly Covariant Theory,” Phys. Rev.162, 1195-1239 (1967)

    1967

  43. [50]

    Gravity as the Limit of the Type II Super- string Theory,

    S. Sannan, “Gravity as the Limit of the Type II Super- string Theory,” Phys. Rev. D34, 1749 (1986)

    1986

  44. [51]

    Gravitational Radiation in the Limit of High Frequency. II. Nonlinear Terms and the Ef fective Stress Tensor,

    R. A. Isaacson, “Gravitational Radiation in the Limit of High Frequency. II. Nonlinear Terms and the Ef fective Stress Tensor,” Phys. Rev.166, 1272-1279 (1968)

    1968

  45. [52]

    Resource- efficient digital quantum simulation of d-level systems for photonic, vibrational, and spin-s Hamiltonians,

    N. P. D. Sawaya, T. Menke, T. H. Kyaw, S. Johri, A. Aspuru-Guzik and G. G. Guerreschi, “Resource- efficient digital quantum simulation of d-level systems for photonic, vibrational, and spin-s Hamiltonians,” npj Quantum Inf.6, 49 (2020)

    2020

  46. [53]

    Improving Hamilto- nian encodings with the Gray code,

    O. Di Matteo, A. McCoy, P. Gysbers, T. Miyagi, R. M. Woloshyn and P. Navr´ atil, “Improving Hamilto- nian encodings with the Gray code,” Phys. Rev. A103, no.4, 042405 (2021)

    2021

  47. [54]

    Theory of Trotter Error with Commutator Scaling,

    A. M. Childs, Y. Su, M. C. Tran, N. Wiebe and S. Zhu, “Theory of Trotter Error with Commutator Scaling,” Phys. Rev. X11, no.1, 011020 (2021)

    2021

  48. [55]

    A bound on chaos,

    J. Maldacena, S. H. Shenker and D. Stanford, “A bound on chaos,” JHEP08, 106 (2016)

    2016

  49. [56]

    Thermalization and its mechanism for generic isolated quantum sys- tems,

    M. Rigol, V. Dunjko and M. Olshanii, “Thermalization and its mechanism for generic isolated quantum sys- tems,” Nature452, no.7189, 854-858 (2008)

    2008

  50. [57]

    Quantum statistical mechanics in a closed system,

    J. M. Deutsch, “Quantum statistical mechanics in a closed system,” Phys. Rev. A43, no.4, 2046 (1991)

  51. [58]

    Chaos and Quantum Thermalization,

    M. Srednicki, “Chaos and Quantum Thermalization,” Phys. Rev. E50, 888

  52. [59]

    From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics,

    L. D’Alessio, Y. Kafri, A. Polkovnikov and M. Rigol, “From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics,” Adv. Phys. 65, no.3, 239-362 (2016)

    2016

  53. [60]

    Average entropy of a subsystem,

    D. N. Page, “Average entropy of a subsystem,” Phys. Rev. Lett.71, 1291-1294 (1993)

    1993

  54. [61]

    Localization of inter- acting fermions at high temperature,

    V. Oganesyan and D. A. Huse, “Localization of inter- acting fermions at high temperature,” Phys. Rev. B75, no.15, 155111 (2007)

    2007

  55. [62]

    Dis- tribution of the Ratio of Consecutive Level Spacings in Random Matrix Ensembles,

    Y. Y. Atas, E. Bogomolny, O. Giraud and G. Roux, “Dis- tribution of the Ratio of Consecutive Level Spacings in Random Matrix Ensembles,” Phys. Rev. Lett.110, no.8, 084101 (2013)

    2013

  56. [63]

    IBM Quantum, device specifications and develop- ment roadmap,https://www.ibm.com/quantum(ac- cessed 2026)

    2026

  57. [64]

    Evidence for the utility of quantum computing before fault tolerance,

    Y. Kim, A. Eddins, S. Anand, K. X. Wei, E. van den Berg, S. Rosenblatt, H. Nayfeh, Y. Wu, M. Zaletel, K. Temme, and A. Kandala, “Evidence for the utility of quantum computing before fault tolerance,” Nature 618, 500 (2023)

    2023

  58. [65]

    Density matrix formulation for quantum renormalization groups,

    S. R. White, “Density matrix formulation for quantum renormalization groups,” Phys. Rev. Lett.69, 2863-2866 (1992)

    1992

  59. [66]

    The density-matrix renormalization group in the age of matrix product states,

    U. Schollwoeck, “The density-matrix renormalization group in the age of matrix product states,” Annals Phys. 326, 96-192 (2011)

    2011

  60. [67]

    Fast Scramblers,

    Y. Sekino and L. Susskind, “Fast Scramblers,” JHEP10, 065 (2008)

    2008

  61. [69]

    V erification of the vanishing theorem and the derived weight The direct cubic expansion of Sec. IV was carried out and cross-checked by three independent engines.En- gine A (symbolic Lagrangian).Inserting the two-block near-horizon metric into √−g Rand collectingO(κ 3) yields...

  62. [70]

    Two independent quantities set the size of such a register, and they constrain the physics in very different ways

    The size of the simulated system and the origin of its limitations The production simulations use theℓ= 2 multiplet (five modes, ten qubits) and theℓ= 2⊕3 register (twelve modes), with a per-mode occupation cutoffd= 4 for production andd= 5,6 as convergence overlays. Two indep...

  63. [71]

    , ℓmax con- tains M(ℓ max) = ℓmaxX ℓ=2 (2ℓ+ 1) = (ℓ max + 1)2 −4 (H1) angular-momentum modes, each mapped ton b = ⌈log2 d⌉qubits, so the register occupiesM n b qubits

    Qubit and gate budgets for larger registers A register spanning the multipolesℓ= 2, . . . , ℓmax con- tains M(ℓ max) = ℓmaxX ℓ=2 (2ℓ+ 1) = (ℓ max + 1)2 −4 (H1) angular-momentum modes, each mapped ton b = ⌈log2 d⌉qubits, so the register occupiesM n b qubits. The number of indep...

  64. [72]

    Accommodation is not a constraint

    F easibility of large-register hardware execution Enlarging the register raises two separate hardware questions with opposite answers: whether the qubits can be accommodated, and whether the resulting circuit can be executed with useful fidelity. Accommodation is not a constra...

  65. [73]

    H 1 all trace to the small ef- fective dimension and small sector sizes of the accessible registers

    Physics accessible only to larger systems The limitations of Sec. H 1 all trace to the small ef- fective dimension and small sector sizes of the accessible registers. Enlarging the register removes both restric- tions and opens four physical questions that the present system c...

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.