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REVIEW 4 major objections 4 minor 60 references

The paper proposes that the exponentiating soft factor that packages Kerr's multipoles also generates a parity-alternating tower of Bondi-frame shifts whose composition law, after a chiral projection, is the classical w1+∞ bracket.

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2026-08-01 07:24 UTC pith:N2DEPEJN

load-bearing objection Plausible central conjecture, correct low-order checks, but the full w1+∞ claim is not yet proven—the higher-spin algebra acts on symbols the Kerr matching doesn't fix. the 4 major comments →

arxiv 2607.27469 v1 pith:N2DEPEJN submitted 2026-07-29 hep-th gr-qchep-ph

w_(1+infty) as the Frame Algebra of Kerr Soft Dressing

Gabriel Menezes This is my paper
classification hep-th gr-qchep-ph
keywords w1+∞ algebraKerr black holesoft graviton theoremsBondi framesupertranslationmemory effectsasymptotic symmetries
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 is trying to establish that the w1+∞ algebra is not just a bookkeeping device for soft graviton modes: it is the composition law of the frame shifts that convert the canonical Bondi frame into the intrinsic frame of Kerr black-hole scattering. The engine is the exponentiating soft factor e^{ηωa·q}, which packages the Kerr multipole tower and splits into even (electric/mass) and odd (magnetic/current) parity parts. The paper shows that this factor selects a tower of supertranslation-like parameters, fixes each one through the inverse problem K^{(s,0)}_AB[t_s]=2G S^{(s)}_{AB,exp}, and solves the tower in closed form (hyperbolic integrals) when the spin is aligned. The observable payoff is a concrete hierarchy of gravitational memory moments — displacement memory at leading order, spin memory at subleading order, and higher electric and magnetic moments beyond — with a computable ratio between the first two.

Core claim

Claim: the exponentiating soft factor e^{ηωa·q} (the Kerr multipole generator) fixes a parity-alternating tower of frame shifts via K^{(s,0)}_AB[t_s]=2G S^{(s)}_{AB,exp}, solved in closed form for aligned spin by hyperbolic integrals, with the s=0 member the VV supertranslation 2G(p·q)log(p·q). Their composition is the Poisson bracket on T^*S^2, which under a chiral projection is the classical w1+∞ bracket: w1+∞ acts on the Kerr soft dressings that map the canonical Bondi frame to the intrinsic scattering frame.

What carries the argument

The load-bearing object is the exponentiating soft factor e^{ηωa·q} — the exponential that generates the Kerr multipoles M_ℓ+iS_ℓ=M(ia)^ℓ — used as the source S^{(s)}_{AB,exp} at each soft order. Its even/odd split under helicity fixes the tower's parity: even levels electric (mass) shifts, odd levels magnetic (current) shifts. The frame equation K^{(s,0)}_AB[t_s]=2G S^{(s)}_{AB,exp} turns the soft charge kernel into an inverse problem for the shift parameter t_s; for aligned spin the tower reduces to two ODEs solved in closed form by hyperbolic integrals (22). The algebra enters through the principal-symbol bracket on T^*S^2; keeping only holomorphic symbols (a local chiral projection) give

Load-bearing premise

The central claim depends on two unproven ingredients: the assumed existence of the higher-spin transformation operators for s≥2 (which the paper says is 'assumed rather than constructed') and the restriction of the closed-form solution to aligned spin, with a residual opposite-parity source left unfixed for generic orientations.

What would settle it

Compute the s=2 sub-subleading soft factor for Kerr scattering and check whether its Kerr-selected, parity-projected part equals 2G S^{(0)}_AB (a·q)^2/2 as predicted by (18); a mismatch would falsify the identification. Independently, attempt to construct the s=2 shift operator with principal symbol t^{AB}D_AD_B and test closure of two such operators against the Schouten bracket plus trace and curvature descendants: if no such operator exists or the bracket fails to close, the w1+∞ frame-algebra claim reduces to a statement about principal symbols only. Also, the magnetic (spin) memory in the

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

If this is right

  • The leading-order prediction is recovered: the s=0 member is exactly the VV supertranslation T_VV=2G(p·q)log(p·q), reproducing the known map from the canonical Bondi frame to the intrinsic frame.
  • The subleading s=1 sector is fixed as the magnetic (divergence-free) part of a generalized-BMS vector; it sources spin memory, while the electric centre-of-mass partner is left undetermined.
  • If the assumed higher-spin operators exist and close, equations (36)-(37) upgrade w1+∞ from an organization of soft insertions to an algebra of frame data on the radiative phase space, with a possible field-dependent extension tied to memory boundary terms.
  • The ratio of the subleading magnetic source to the leading electric source is ωa·q = χ(GMω)γ(v−cosθ), reaching tens of percent for plausible merger parameters and vanishing at the aberration angle cosθ=v.
  • The Kerr spin exponential acts as a generating function for a sequence of memory moments (displacement, spin, higher electric and magnetic memories) measured by the regulated memory probes defined in the paper.

Where Pith is reading between the lines

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

  • Editorial inference: if the assumed s≥2 operators are constructed and close with their trace and curvature descendants, w1+∞ would become a genuine asymptotic symmetry of the radiative phase space in the Kerr sector, and the extension K_{s,s'} in (37) could encode nonlinear memory data beyond universal soft terms.
  • Editorial inference: the closed-form aligned solution (22) predicts a sharp observational signature — magnetic (spin) memory should vanish on the sphere at cosθ=v, the aberration direction where the sinh source has its zero — that could be searched for in waveform models.
  • Editorial inference: the parity-alternating structure mirrors the Kerr multipole split, so the residual opposite-parity pieces left unfixed for generic spin orientation might be fixed by the same w1+∞ closure requirement, extending the frame dictionary to arbitrary spin direction.
  • Editorial inference: because the identification is made at leading order in G and for the universal soft sector only, the same frame-dictionary logic could be iterated at higher post-Minkowskian orders, where the algebra would govern the transformation between radiative and intrinsic frames beyond the sector the paper treats.

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

4 major / 4 minor

Summary. The paper argues that the Veneziano–Vilkovisky (VV) supertranslation, extended to higher soft orders, gives a parity-alternating tower of frame shifts whose generating function is the Kerr spin exponential e^{ηω a·q}. After a chiral projection, the composition law of these shifts is claimed to be the classical w_{1+∞} bracket. The s=0 and s=1 cases are checked against known results: the s=0 kernel reproduces the VV shift T_VV = 2G(p·q) log(p·q), and the s=1 kernel gives the magnetic (spin-memory) projection of a generalized BMS vector. For aligned spin, the tower is solved in closed form in terms of hyperbolic integrals (Eq. 22), yielding explicit electric and magnetic potentials. The central claim is that the algebra acting on these Kerr-selected soft dressings is w_{1+∞}, with the polynomial Poisson algebra on T*S² as the global statement.

Significance. If fully established, the result would give a concrete physical interpretation of w_{1+∞} as the frame-algebra of Kerr soft dressings, thereby connecting celestial symmetry algebras to black-hole scattering dynamics. The paper has clear strengths: the s=0 and s=1 checks are explicitly matched to known literature; the aligned-spin ODE solution (22) is closed-form and internally consistent; the matching to the Kerr no-hair relation via the exponentiating soft factor is well motivated; and the authors are admirably explicit about the limitations of the construction. However, the central higher-spin claim rests on unproven assumptions: the existence of the homogeneous operators L_t^{(s)} for s≥2, the closure of the bracket (36) without a field-dependent extension, and the resolution of the underdetermination of the STF parameter t by the matching equation. The paper's own disclaimers in the End Matter and §"Algebra after the charges" make these gaps clear. At present, the evidence is strong for the low-spin sector and for a principal-symbol conjecture, but not for the full w_{1+∞} frame-algebra claim.

major comments (4)
  1. [Algebra after the charges / Eq. (36)] The bracket (36) is defined on full STF symbols F_t = t^{A1...As} p_{A1}...p_{As}, but the matching equation (18) fixes only the parity-projected scalar χ_t^{(s)} of Eq. (14). For s≥2 an STF rank-s tensor carries more data than this scalar, as the text itself concedes ('an STF rank-s tensor carries two potentials while the inverse problem fixes one'). Consequently, two different parameters t with the same χ_t^{(s)} produce the same frame shift K^{(s,0)}_{AB}[t] but different symbols F_t. The composition law (36) is therefore not a statement about the actual Kerr-selected frame parameters; it is a statement about an underdetermined formal symbol. This is the load-bearing gap in the central claim that w_{1+∞} acts on Kerr soft dressings.
  2. [End Matter, Charge bracket / Eq. (37)] The homogeneous transformation operators L_t^{(s)} for s≥2 are assumed, not constructed: the End Matter states 'Its existence for s≥2 is assumed rather than constructed.' The bracket (36) uses only the principal symbol, and Eq. (37) leaves open a possible field-dependent extension K_{s,s'}[t,t';C]. Until these operators and their closure are explicitly exhibited, the identification of the charge algebra with w_{1+∞} holds only at the level of principal symbols, not as a theorem about the frame shifts (29) that are the paper's physical output.
  3. [Leading and subleading checks / footnote 1] The inverse problem is solved only for aligned spin. Footnote 1 states that for generic spin orientation a residual opposite-parity piece survives at each level and is not fixed. Thus the all-orders solution (22) and the parity-alternating tower (23) apply only to the aligned configuration. The claim that the parity alternation exactly matches the Kerr multipoles (electric at even s, magnetic at odd s) is therefore verified only in a restricted kinematic sector, and the extension to generic spin is not provided.
  4. [One may still recover... / Eq. (27)] The chiral projection that yields the classical w_{1+∞} bracket (27) is local, and the text explicitly says it is 'not the same as the real global Kerr frame shift, whose vector is generically smooth and non-holomorphic.' Therefore the statement that w_{1+∞} is the frame algebra of Kerr soft dressing is made only after a projection that changes the objects. The global statement is the more conservative polynomial Poisson algebra on T*S², which is not the same as w_{1+∞} except in a local chiral patch. This limitation should be foregrounded in the title and abstract if the higher-spin gaps remain unresolved.
minor comments (4)
  1. [Abstract] Typo: 'it leads a tower' should be 'it leads to a tower' or 'it yields a tower.'
  2. [Eq. (15)] For odd s, χ_t^{(s)} in Eq. (14) already contains an epsilon factor; writing K^{(s,0)}_{AB} = eD_{AB} χ_t^{(s)} in Eq. (15) may double-count the curl. Please clarify the convention so that the s=1 case (20) is manifestly consistent.
  3. [Fig. 1] In the caption, the dotted line marks the zero of Ψ''_ω, not of Ψ_ω. Consider making this explicit to avoid confusion, since the figure shows Ψ/2G.
  4. [References] Reference [37] (Andrade e Silva and Speziale) is cited as arXiv:2605.13804; if this is a preprint under review, indicate its status. The other 2026 citations are fine.

Circularity Check

1 steps flagged

Eq. (18) makes 'Kerr selection' of the tower equal to the source by construction; the w1+∞ bracket itself is independent but its action on the underdetermined frame data is not established.

specific steps
  1. self definitional [Eq. (18) in 'Soft charges, differential kernels and Kerr motivation'; see also abstract 'We show it leads a tower selected...']
    "The identification proposed here is K^{(s,0)}_{AB}[t] = 2G S^{(s)}_{AB,exp}, where the right-hand side is the Kerr-selected exponentiating projection of the universal soft contribution ... This is not an arbitrary prescription."

    The 'selection' of the tower is not derived from a first-principles soft theorem: the kernel is defined to equal 2G times the exponentiating Kerr source. Because S^{(s)}_{exp} is already the cosh/sinh split of e^{ηωa·q} (Eqs. 11–13), the resulting parity alternation and the 'Kerr-selected' character of the tower are built into the matching condition (18) itself. The abstract's 'We show it leads a tower selected by the exponentiating soft expansion' therefore restates the identification rather than demonstrating a consequence of it. The later closed-form solution (22) and the bracket (36) are meaningful, but they act on objects whose Kerr-selected nature was fixed by the same equation that is presented as the discovery.

full rationale

Most of the derivation is self-contained and not circular. The aligned-spin solutions (22)–(23) are genuine closed-form solutions of the differential equations obtained after the matching, and the bracket (36) is the standard principal-symbol Poisson structure on T*S^2 whose chiral reduction to w1+∞ (27) is an external mathematical fact; neither depends on fitting parameters to the Kerr source. I find no load-bearing self-citation: refs. [15,51,60] are external, and the deferred 'companion paper' is a promise of future support rather than circular evidence. However, at Eq. (18) the central word 'selected' is definitional: the kernel is equated with 2G times the exponentiating Kerr source, so the parity alternation announced in the abstract is a restatement of the chosen identification, not an independent derivation. The paper is transparent in calling (18) 'the identification proposed here,' which keeps this from being a severe circularity. Separately, the passage from (18) to the algebra is not fully supported: the paper admits 'Its existence for s≥2 is assumed rather than constructed' and 'For s≥2 an STF rank-s tensor carries two potentials while the inverse problem fixes one,' so the w1+∞ bracket acts on full STF symbols that the inverse problem does not determine. That is a correctness/rigor gap rather than a circularity, and I have weighted it in the verdict without adding it to the circularity score. Overall: one definitional 'selection' step, with the algebra content still independent, gives a modest score of 3.

Axiom & Free-Parameter Ledger

3 free parameters · 6 axioms · 0 invented entities

No new particles, forces, or conserved quantities are introduced. No numerical constants are fitted to data. The central claim rests instead on several stipulated constructions: the higher-spin charge tower and the identification (18), the assumed existence of L_t^{(s)} for s≥2, and the aligned-spin restriction. These are honest assumptions, but they are load-bearing.

free parameters (3)
  • λ (soft bookkeeper) = ω (soft frequency)
    Introduced as an inverse-length bookkeeper and then set equal to the soft frequency after the level expansion (Eq. 11). Not fitted to data; a bookkeeping scale.
  • Reference scale μ in log(p·q/μ) = arbitrary
    Changing μ adds a term proportional to x=p·q, which is exactly a translation ambiguity in T_VV (text after Eq. 6). Gauge freedom, not a fitted parameter.
  • Translation-fixing normalization of Φ_λ, Ψ_λ = vanishing at cosθ=0 with first derivative
    Adopted in Fig. 1 to fix the translation ambiguity; not fitted to data and does not affect physical shifts.
axioms (6)
  • ad hoc to paper There exists a tower of soft charges Q_s(t) with field-independent kernels K^{(s,0)} of the form (15), including trace/curvature descendants, for all s≥0.
    Postulated; the s≥2 component is not constructed and is deferred to a companion paper (End Matter, 'Charge bracket').
  • ad hoc to paper The soft kernel equals the Kerr-selected exponentiating soft factor: K^{(s,0)}[t] = 2G S^{(s)}_{AB,exp} (Eq. 18).
    Called 'the identification proposed here'; it is exact at s=0 and matched at s=1, but for s≥2 it is a defining selection of one soft sector.
  • ad hoc to paper The homogeneous transformation operators L_t^{(s)} for s≥2 exist and close; the charge bracket (37) closes up to a possible field-dependent extension K_{s,s'}.
    The existence is 'assumed rather than constructed' (End Matter, 'Charge bracket').
  • domain assumption For aligned spin, the source is fully captured by parity-projecting the exponential e^{ηωa·q}; generic spin orientation is not addressed.
    The paper explicitly limits the solved statement to aligned spin (footnote 1: consistency only when y is a function of x).
  • domain assumption The leading VV dictionary D^{AB}T_VV = 2G S^{(0)}_{AB} and the identification of T_VV with the exponent of the leading Faddeev–Kulish dressing are taken from Refs [15,40-44].
    Background from prior literature; used as the starting point and not re-derived in this paper.
  • domain assumption The classical Kerr source S^{(0)} e^{ηωa·q} equals the Guevara–Ochirov–Vines exponential on three-point support, via Ref. [51,54-56] and the Newman–Janis complex shift.
    Imported from amplitude literature; the paper checks sign conventions and three-point support, but the identity itself is prior work.

pith-pipeline@v1.3.0-daily-deepseek · 13453 in / 16084 out tokens · 152156 ms · 2026-08-01T07:24:24.343198+00:00 · methodology

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read the original abstract

The Veneziano--Vilkovisky supertranslation is the residual large diffeomorphism relating the canonical Bondi frame to the intrinsic frame of the scattering bodies. We show it leads a tower selected by the exponentiating soft expansion, the object generating the Kerr multipoles at three points. Since \(e^{\eta\omega a\cdot q}\) splits into even and odd parts, the tower alternates parity, and for aligned spin we solve it to all orders in hyperbolic integrals. After a chiral projection its composition law is the classical $w_{1+\infty}$ bracket: the physical content we assign to that algebra.

Figures

Figures reproduced from arXiv: 2607.27469 by Gabriel Menezes.

Figure 1
Figure 1. Figure 1: FIG. 1. Aligned-spin frame generators from ( [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

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Reference graph

Works this paper leans on

60 extracted references · 52 linked inside Pith

  1. [1]

    Kapec, P

    D. Kapec, P. Mitra, A.-M. Raclariu, and A. Strominger, A 2D Stress Tensor for 4D Gravity, Phys.Rev.Lett.119, 121601 (2017), arXiv:1609.00282 [hep-th]. 6

    Pith/arXiv arXiv 2017

  2. [2]

    Guevara, E

    A. Guevara, E. Himwich, M. Pate, and A. Strominger, Holographic Symmetry Algebras for Gauge Theory and Gravity, JHEP11, 152 (2021), arXiv:2103.03961 [hep- th]

    Pith/arXiv arXiv 2021

  3. [3]

    Strominger,w 1+∞ and the Celestial Sphere, Phys

    A. Strominger,w 1+∞ and the Celestial Sphere, Phys. Rev. Lett.127, 221601 (2021), arXiv:2105.14346 [hep- th]

    Pith/arXiv arXiv 2021

  4. [4]

    Hamada and G

    Y. Hamada and G. Shiu,Infinite Set of Soft Theorems in Gauge-Gravity Theories as Ward-Takahashi Identities, Phys. Rev. Lett.120, 201601 (2018), arXiv:1801.05528 [hep-th]

    Pith/arXiv arXiv 2018

  5. [5]

    Li, H.-H

    Z.-Z. Li, H.-H. Lin, and S.-Q. Zhang,Infinite Soft The- orems from Gauge Symmetry, Phys. Rev. D98, 045004 (2018), arXiv:1802.03148 [hep-th]

    Pith/arXiv arXiv 2018

  6. [6]

    E.HimwichandM.Pate,w 1+∞ in 4D Gravitational Scat- tering, JHEP07, 180 (2024), arXiv:2312.08597 [hep-th]

    Pith/arXiv arXiv 2024

  7. [7]

    Pasterski, S.-H

    S. Pasterski, S.-H. Shao, and A. Strominger,Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere, Phys. Rev. D96, 065026 (2017), arXiv:1701.00049 [hep-th]

    Pith/arXiv arXiv 2017

  8. [8]

    Pasterski and S.-H

    S. Pasterski and S.-H. Shao,A Conformal Basis for Flat Space Amplitudes, Phys. Rev. D96, 065022 (2017), arXiv:1705.01027 [hep-th]

    Pith/arXiv arXiv 2017

  9. [9]

    S.Pasterski,Lectures on Celestial Amplitudes, Eur.Phys. J. C81, 1062 (2021), arXiv:2108.04801 [hep-th]

    Pith/arXiv arXiv 2021

  10. [10]

    Donnay, S

    L. Donnay, S. Pasterski, and A. Puhm,Goldilocks Modes and the Three Scattering Bases, JHEP06, 124 (2022), arXiv:2202.11127 [hep-th]

    Pith/arXiv arXiv 2022

  11. [11]

    Hu and S

    Y. Hu and S. Pasterski,Detector Operators for Celes- tial Symmetries, JHEP12, 035 (2023), arXiv:2307.16801 [hep-th]

    Pith/arXiv arXiv 2023

  12. [12]

    Freidel, D

    L. Freidel, D. Pranzetti, and A.-M. Raclariu,Higher spin dynamics in gravity andw1+∞ celestial symmetries, Phys. Rev. D106, 086013 (2022), arXiv:2112.15573 [hep- th]

    Pith/arXiv arXiv 2022

  13. [13]

    Geiller,Celestialw 1+∞ charges and the subleading structure of asymptotically-flat spacetimes, SciPost Phys

    M. Geiller,Celestialw 1+∞ charges and the subleading structure of asymptotically-flat spacetimes, SciPost Phys. 18, 023 (2025), arXiv:2403.05195 [hep-th]

    Pith/arXiv arXiv 2025

  14. [14]

    Donnay, L

    L. Donnay, L. Freidel, and Y. Herfray,CarrollianLw1+∞ representation from twistor space, SciPost Phys.17, 118 (2024), arXiv:2402.00688 [hep-th]

    Pith/arXiv arXiv 2024

  15. [15]

    Elkhidir, D

    A. Elkhidir, D. O’Connell, and R. Roiban,Supertransla- tions from Scattering Amplitudes, Phys. Rev. Lett.135, 151601 (2025), arXiv:2408.15961 [hep-th]

    Pith/arXiv arXiv 2025

  16. [16]

    Cheung, I

    C. Cheung, I. Z. Rothstein, and M. P. Solon,From Scat- tering Amplitudes to Classical Potentials in the Post- Minkowskian Expansion, Phys. Rev. Lett.121, 251101 (2018), arXiv:1808.02489 [hep-th]

    Pith/arXiv arXiv 2018

  17. [17]

    D. A. Kosower, B. Maybee, and D. O’Connell,Ampli- tudes, Observables, and Classical Scattering, JHEP02, 137 (2019), arXiv:1811.10950 [hep-th]

    Pith/arXiv arXiv 2019

  18. [18]

    Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon, and M. Zeng,Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order, Phys. Rev. Lett.122, 201603 (2019), arXiv:1901.04424 [hep-th]

    Pith/arXiv arXiv 2019

  19. [19]

    Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon, andM.Zeng,Black Hole Binary Dynamics from the Dou- ble Copy and Effective Theory, JHEP10, 206 (2019), arXiv:1908.01493 [hep-th]

    Pith/arXiv arXiv 2019

  20. [20]

    Cristofoli, R

    A. Cristofoli, R. Gonzo, D. A. Kosower, and D. O’Connell,Waveforms from Amplitudes, Phys. Rev. D 106, 056007 (2022), arXiv:2107.10193 [hep-th]

    Pith/arXiv arXiv 2022

  21. [21]

    E.Herrmann, J.Parra-Martinez, M.S.Ruf, andM.Zeng, Radiative Classical Gravitational Observables atO(G 3) from Scattering Amplitudes, JHEP10, 148 (2021), arXiv:2104.03957 [hep-th]

    Pith/arXiv arXiv 2021

  22. [22]

    Buonanno, M

    A. Buonanno, M. Khalil, D. O’Connell, R. Roiban, M. P. Solon, and M. Zeng,Snowmass White Pa- per: Gravitational Waves and Scattering Amplitudes, arXiv:2204.05194 [hep-th]

    Pith/arXiv arXiv

  23. [23]

    Aoude, K

    R. Aoude, K. Haddad, C. Heissenberg, and A. Helset, Leading-order gravitational radiation to all spin orders, Phys. Rev. D109, 036007 (2024), arXiv:2310.05832 [hep- th]

    Pith/arXiv arXiv 2024

  24. [24]

    Georgoudis, C

    A. Georgoudis, C. Heissenberg, and R. Russo,An eikonal-inspired approach to the gravitational scattering waveform, JHEP03, 089 (2024), arXiv:2312.07452 [hep- th]

    Pith/arXiv arXiv 2024

  25. [25]

    Georgoudis, V

    A. Georgoudis, V. Goncalves, C. Heissenberg, and J. Parra-Martinez,Nonlinear Gravitational Memory in the Post-Minkowskian Expansion, Phys. Rev. Lett.136, 121401 (2026), arXiv:2506.20733 [hep-th]

    Pith/arXiv arXiv 2026

  26. [26]

    Barnich and C

    G. Barnich and C. Troessaert,Aspects of the BMS/CFT correspondence, JHEP05, 062 (2010), arXiv:1001.1541 [hep-th]

    Pith/arXiv arXiv 2010

  27. [27]

    Campiglia and A

    M. Campiglia and A. Laddha,Asymptotic symmetries and subleading soft graviton theorem, Phys. Rev. D90, 124028 (2014), arXiv:1408.2228 [hep-th]

    Pith/arXiv arXiv 2014

  28. [28]

    Campiglia and A

    M. Campiglia and A. Laddha,New symmetries for the Gravitational S-matrix, JHEP04, 076 (2015), arXiv:1502.02318 [hep-th]

    Pith/arXiv arXiv 2015

  29. [29]

    Campiglia and A

    M. Campiglia and A. Laddha,Asymptotic symmetries of gravity and soft theorems for massive particles, JHEP12, 094 (2015), arXiv:1509.01406 [hep-th]

    Pith/arXiv arXiv 2015

  30. [30]

    Compere, A

    G. Compere, A. Fiorucci, and R. Ruzziconi,Superboost transitions, refraction memory and super-Lorentz charge algebra, JHEP11, 200 (2018); Erratum: JHEP04, 172 (2020), arXiv:1810.00377 [hep-th]

    Pith/arXiv arXiv 2018

  31. [31]

    Strominger,On BMS Invariance of Gravitational Scattering, JHEP07, 152 (2014), arXiv:1312.2229 [hep- th]

    A. Strominger,On BMS Invariance of Gravitational Scattering, JHEP07, 152 (2014), arXiv:1312.2229 [hep- th]

    Pith/arXiv arXiv 2014

  32. [32]

    T. He, V. Lysov, P. Mitra, and A. Strominger,BMS supertranslations and Weinberg’s soft graviton theorem, JHEP05, 151 (2015), arXiv:1401.7026 [hep-th]

    Pith/arXiv arXiv 2015

  33. [33]

    Strominger and A

    A. Strominger and A. Zhiboedov,Gravitational Mem- ory, BMS Supertranslations and Soft Theorems, JHEP 01, 086 (2016), arXiv:1411.5745 [hep-th]

    Pith/arXiv arXiv 2016

  34. [34]

    Strominger,Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448 [hep-th]

    A. Strominger,Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448 [hep-th]

    Pith/arXiv arXiv

  35. [35]

    Pasterski, A

    S. Pasterski, A. Strominger, and A. Zhiboedov, New Gravitational Memories, JHEP12, 053 (2016), arXiv:1502.06120 [hep-th]

    Pith/arXiv arXiv 2016

  36. [36]

    S. Choi, A. Laddha, and A. Puhm,Asymptotic Symme- tries for Logarithmic Soft Theorems in Gauge Theory and Gravity, arXiv:2403.13053 [hep-th]

    Pith/arXiv arXiv

  37. [37]

    Andrade e Silva and S

    R. Andrade e Silva and S. Speziale,An algebra of proper observables at null infinity: Dirac brackets, Memory and Goldstone probes, arXiv:2605.13804 [hep-th]

    Pith/arXiv arXiv

  38. [38]

    Bondi, M

    H. Bondi, M. G. J. van der Burg, and A. W. K. Metzner, Gravitational waves in general relativity. VII. Waves from axi-symmetric isolated systems, Proc. Roy. Soc. Lond. A269, 21 (1962)

    1962

  39. [39]

    R. K. Sachs,Gravitational waves in general relativity. VIII. Waves in asymptotically flat space-time, Proc. Roy. Soc. Lond. A270, 103 (1962). 7

    1962

  40. [40]

    Veneziano and G

    G. Veneziano and G. A. Vilkovisky,Angular momentum loss in gravitational scattering, radiation reaction, and the Bondi gauge ambiguity, Phys. Lett. B834, 137419 (2022), arXiv:2201.11607 [gr-qc]

    Pith/arXiv arXiv 2022

  41. [41]

    Damour,Radiative contribution to classical gravita- tional scattering at the third order inG, Phys

    T. Damour,Radiative contribution to classical gravita- tional scattering at the third order inG, Phys. Rev. D 102, 124008 (2020), arXiv:2010.01641 [gr-qc]

    Pith/arXiv arXiv 2020

  42. [42]

    P. P. Kulish and L. D. Faddeev,Asymptotic condi- tions and infrared divergences in quantum electrodynam- ics, Theor. Math. Phys.4, 745 (1970)

    1970

  43. [43]

    J. Ware, R. Saotome, and R. Akhoury,Construction of an asymptotic S matrix for perturbative quantum gravity, JHEP10, 159 (2013), arXiv:1308.6285 [hep-th]

    Pith/arXiv arXiv 2013

  44. [44]

    Choi and R

    S. Choi and R. Akhoury,Subleading soft dressings of asymptotic states in QED and perturbative quantum grav- ity, JHEP09, 031 (2019), arXiv:1907.05438 [hep-th]

    Pith/arXiv arXiv 2019

  45. [45]

    Ashtekar and M

    A. Ashtekar and M. Streubel,Symplectic Geometry of Radiative Modes and Conserved Quantities at Null Infin- ity, Proc. Roy. Soc. Lond. A376, 585 (1981)

    1981

  46. [46]

    Weinberg,Infrared photons and gravitons, Phys

    S. Weinberg,Infrared photons and gravitons, Phys. Rev. 140, B516 (1965)

    1965

  47. [47]

    Cachazo and A

    F. Cachazo and A. Strominger,Evidence for a New Soft Graviton Theorem, arXiv:1404.4091 [hep-th]

    Pith/arXiv arXiv

  48. [48]

    Z. Bern, S. Davies, P. Di Vecchia, and J. Nohle, Low-Energy Behavior of Gluons and Gravitons from Gauge Invariance, Phys. Rev. D90, 084035 (2014), arXiv:1406.6987 [hep-th]

    Pith/arXiv arXiv 2014

  49. [49]

    Campiglia and A

    M. Campiglia and A. Laddha,Sub-subleading soft gravi- tons: New symmetries of quantum gravity?, Phys. Lett. B764, 218 (2017), arXiv:1605.09094 [gr-qc]

    Pith/arXiv arXiv 2017

  50. [50]

    A.LaddhaandA.Sen,Sub-subleading Soft Graviton The- orem in Generic Theories of Quantum Gravity, JHEP 10, 065 (2017), arXiv:1706.00759 [hep-th]

    Pith/arXiv arXiv 2017

  51. [51]

    Guevara, A

    A. Guevara, A. Ochirov, and J. Vines,Scattering of Spin- ning Black Holes from Exponentiated Soft Factors, JHEP 09, 056 (2019), arXiv:1812.06895 [hep-th]

    Pith/arXiv arXiv 2019

  52. [52]

    Compere, R

    G. Compere, R. Oliveri, and A. Seraj,Metric recon- struction from celestial multipoles, JHEP10, 001 (2022), arXiv:2206.12597 [gr-qc]

    Pith/arXiv arXiv 2022

  53. [53]

    M. M. Riva, F. Vernizzi, and L. K. Wong,Angular momentum balance in gravitational two-body scattering: Flux, memory, and supertranslation invariance, Phys. Rev. D108, 104052 (2023), arXiv:2302.09065 [gr-qc]

    Pith/arXiv arXiv 2023

  54. [54]

    Arkani-Hamed, T.-C

    N. Arkani-Hamed, T.-C. Huang, and Y.-t. Huang,Scat- tering Amplitudes For All Masses and Spins, JHEP11, 070 (2021), arXiv:1709.04891 [hep-th]

    Pith/arXiv arXiv 2021

  55. [55]

    Guevara,Holomorphic Classical Limit for Spin Effects in Gravitational and Electromagnetic Scattering, JHEP 04, 033 (2019), arXiv:1706.02314 [hep-th]

    A. Guevara,Holomorphic Classical Limit for Spin Effects in Gravitational and Electromagnetic Scattering, JHEP 04, 033 (2019), arXiv:1706.02314 [hep-th]

    Pith/arXiv arXiv 2019

  56. [56]

    Guevara, A

    A. Guevara, A. Ochirov, and J. Vines,Black-hole scattering with general spin directions from minimal- coupling amplitudes, Phys. Rev. D100, 104024 (2019), arXiv:1906.10071 [hep-th]

    Pith/arXiv arXiv 2019

  57. [57]

    R. P. Geroch,Multipole moments. I. Flat space, J. Math. Phys.11, 2580 (1970)

    1970

  58. [58]

    R. O. Hansen,Multipole moments of stationary space- times, J. Math. Phys.15, 46 (1974)

    1974

  59. [59]

    K. S. Thorne,Multipole Expansions of Gravitational Ra- diation, Rev. Mod. Phys.52, 299 (1980)

    1980

  60. [60]

    END MA TTER Kerr three-point amplitude and multipole check.This restriction is physically motivated by Kerr black holes

    A.Guevara,Gravity From a Color Symmetry II: Celestial Color Kinematics for Mass and Spin,2412.19641[hep- th]. END MA TTER Kerr three-point amplitude and multipole check.This restriction is physically motivated by Kerr black holes. At the amplitude level the spinning three-point object is an operator on massive spin states [51, 54–56]. For a soft gravitonk...

    Pith/arXiv arXiv