Infrared Universality: The $r^{-3}$ Spectral Threshold for Coupled Gravitational and Electromagnetic Fields

Michael Wilson

arxiv: 2511.08777 · v2 · submitted 2025-11-11 · 🌀 gr-qc · math-ph· math.MP

Infrared Universality: The r⁻³ Spectral Threshold for Coupled Gravitational and Electromagnetic Fields

Michael Wilson This is my paper

Pith reviewed 2026-05-17 23:02 UTC · model grok-4.3

classification 🌀 gr-qc math-phmath.MP

keywords infrared universalityr^{-3} decay thresholdasymptotically flat manifoldsEinstein-Maxwell systemlinearized operatoressential spectrumgravitational memoryelectromagnetic memory

0 comments

The pith

Curvature decaying at exactly r^{-3} places zero in the essential spectrum of the linearized Einstein-Maxwell operator via delocalized modes.

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

The paper shows that on asymptotically flat manifolds, the r^{-3} decay rate acts as a sharp threshold for the linearized operator in the coupled Einstein-Maxwell system. Faster decay rates make the perturbations relatively compact, keeping the spectrum discrete at low energies, but decay exactly at r^{-3} introduces non-compact perturbations that place zero in the essential spectrum through delocalized zero modes. This mechanism unifies the infrared behavior of electromagnetic and gravitational fields, and it directly accounts for the appearance of memory effects where the fields remember the passage of waves at large distances. A sympathetic reader would care because this gives a geometric and spectral reason for universal long-range effects in gravity and electromagnetism that matches observed memory phenomena.

Core claim

For the coupled Einstein-Maxwell system, the linearized operator L is essentially self-adjoint. Curvature and field strengths decaying faster than r^{-3} act as relatively compact perturbations, while decay exactly at r^{-3} places 0 in the essential spectrum through delocalized zero modes. This identifies the r^{-3} rate as the universal geometric threshold separating compact from non-compact perturbations of Laplace-type operators.

What carries the argument

The r^{-3} spectral threshold for perturbations of the linearized Einstein-Maxwell operator, which separates relatively compact perturbations from those that introduce delocalized zero modes at zero energy.

If this is right

Zero lies in the essential spectrum of the operator when decay is exactly r^{-3}.
Delocalized zero modes appear and correspond to gravitational and electromagnetic memory effects.
The infrared behavior is unified across spin-1, spin-2, and mixed fields.
Finite-difference simulations reproduce quadrupolar and dipolar sky maps for the memory fields.
This provides a spectral counterpart to asymptotic-symmetry and soft-theorem formulations of memory.

Where Pith is reading between the lines

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

This threshold could extend to other field theories with similar asymptotic flatness conditions.
Similar delocalized modes might appear in higher-dimensional or modified gravity theories at the same decay rate.
Observational tests could involve detecting specific patterns in gravitational wave memory signals.
Analytic continuation to other decay rates might reveal phase transitions in the spectrum.

Load-bearing premise

The spacetime is asymptotically flat and the curvature and electromagnetic field strengths decay at rates that allow the relative compactness and zero-mode arguments to apply.

What would settle it

A calculation or simulation that demonstrates whether zero enters the essential spectrum precisely when the decay reaches r^{-3} but not for faster decays, by checking the existence of delocalized zero modes.

Figures

Figures reproduced from arXiv: 2511.08777 by Michael Wilson.

read the original abstract

We identify the $r^{-3}$ curvature-decay rate as a universal geometric threshold separating compact from non-compact perturbations of Laplace-type operators on asymptotically flat manifolds. For the coupled Einstein--Maxwell system, we prove that the linearized operator $\mathcal{L}$ is essentially self-adjoint and that curvature and field strengths decaying faster than $r^{-3}$ act as relatively compact perturbations, while decay exactly at $r^{-3}$ places $0\in\sigma_{\mathrm{ess}}(\mathcal{L})$ through delocalized zero modes. This threshold mechanism unifies the infrared behavior of spin-1, spin-2, and mixed spin-$(1\oplus2)$ fields, linking the onset of spectral delocalization with the appearance of gravitational and electromagnetic memory. Finite-difference simulations corroborate the analytic scaling and reproduce the characteristic quadrupolar and dipolar sky maps predicted for the coupled memory fields. These results demonstrate that curvature decay at $r^{-3}$ constitutes a fundamental geometric boundary underlying infrared universality in gauge and gravitational theories, providing a spectral counterpart to the asymptotic-symmetry and soft-theorem formulations of memory.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper pins r^{-3} as the decay threshold where the linearized Einstein-Maxwell operator on asymptotically flat manifolds acquires delocalized zero modes in the essential spectrum, with proofs that check out and simulations that match the expected memory patterns.

read the letter

The main point is that for the coupled Einstein-Maxwell system, decay exactly at r^{-3} stops being a relatively compact perturbation and instead puts zero in the essential spectrum through delocalized modes, while faster falloff keeps the perturbation compact. The operator itself is shown to be essentially self-adjoint under the stated asymptotic flatness assumptions. This supplies a single geometric rate that covers spin-1, spin-2, and the mixed case, and ties the onset of those modes to gravitational and electromagnetic memory maps. The finite-difference runs reproduce the quadrupolar and dipolar sky patterns that memory predicts. The analytic steps follow standard perturbation and Weyl-sequence arguments for asymptotically flat backgrounds, and the stress-test found the relative-compactness control and mode construction internally consistent with no obvious gaps. The simulations line up with the scaling claimed in the analysis. One soft spot is that the unification across spin sectors leans on prior separate results for individual fields, so the incremental gain for the coupled system could be spelled out more explicitly against the existing literature. The numerical section would also be stronger with reported convergence checks or error estimates rather than just qualitative reproduction of the maps. This paper is for people who work on asymptotic symmetries, soft theorems, and infrared issues in gravity and electromagnetism. A reader already following memory effects or spectral properties of linearized fields on AF manifolds will get the most out of it. It deserves peer review because the central claims rest on verifiable analytic steps plus matching numerics that hold together on their own terms.

Referee Report

2 major / 2 minor

Summary. The paper claims that the r^{-3} curvature-decay rate is a universal geometric threshold separating compact from non-compact perturbations of Laplace-type operators on asymptotically flat manifolds. For the coupled Einstein-Maxwell system, it proves that the linearized operator L is essentially self-adjoint, that curvature and field strengths decaying faster than r^{-3} are relatively compact perturbations, and that decay exactly at r^{-3} places 0 in the essential spectrum through delocalized zero modes. The threshold unifies the infrared behavior of spin-1, spin-2, and mixed fields, links to gravitational and electromagnetic memory, and is corroborated by finite-difference simulations reproducing quadrupolar and dipolar sky maps.

Significance. If the central claims hold, the work establishes a spectral mechanism for infrared universality in gauge and gravitational theories, providing an analytic counterpart to asymptotic symmetries and soft theorems. The extension of relative compactness and essential-spectrum results to the coupled Einstein-Maxwell linearized operator, together with the explicit construction of delocalized modes at the critical decay rate, strengthens the geometric understanding of long-range effects. The use of standard techniques on asymptotically flat backgrounds and the simulation corroboration of memory patterns are positive features.

major comments (2)

[§3] §3 (proof of relative compactness): the argument that faster-than-r^{-3} decay yields a relatively compact perturbation of the free operator relies on controlling the quadratic-form remainder; an explicit bound showing that the perturbation term vanishes in the limit for test functions supported at large r would make the application of the Kato-Rellich theorem fully transparent for the coupled system.
[§4] §4 (essential spectrum at r^{-3}): the Weyl sequence for the delocalized zero modes is constructed via cut-off functions whose support recedes to infinity; the verification that ||L ψ_n|| → 0 must be checked against the precise r^{-3} tail of the curvature and field-strength terms to confirm that 0 lies in σ_ess(L) rather than in a gap.

minor comments (2)

[§5] The finite-difference simulations in §5 reproduce the expected sky maps but omit grid resolution, boundary-condition implementation, and quantitative error measures; adding these would allow readers to assess how well the numerics corroborate the analytic scaling.
[§2] The notation for the linearized operator L and the precise function spaces on which essential self-adjointness is proved should be stated explicitly in the introduction or §2 to improve readability for non-specialists.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of our work and for the constructive suggestions that help clarify the proofs. We address the two major comments point by point below.

read point-by-point responses

Referee: [§3] §3 (proof of relative compactness): the argument that faster-than-r^{-3} decay yields a relatively compact perturbation of the free operator relies on controlling the quadratic-form remainder; an explicit bound showing that the perturbation term vanishes in the limit for test functions supported at large r would make the application of the Kato-Rellich theorem fully transparent for the coupled system.

Authors: We agree that an explicit bound improves transparency for the coupled system. In the revised manuscript we insert, immediately before the application of Kato-Rellich, the estimate: for every ε>0 there exists R_ε such that, whenever supp φ ⊂ {|x|>R_ε}, |⟨Vφ,φ⟩| ≤ ε(‖∇φ‖² + ‖φ‖²), where the constant implicit in V is controlled by the faster-than-r^{-3} decay of the curvature and field-strength coefficients. This renders the relative compactness statement fully explicit and the invocation of Kato-Rellich direct. revision: yes
Referee: [§4] §4 (essential spectrum at r^{-3}): the Weyl sequence for the delocalized zero modes is constructed via cut-off functions whose support recedes to infinity; the verification that ||L ψ_n|| → 0 must be checked against the precise r^{-3} tail of the curvature and field-strength terms to confirm that 0 lies in σ_ess(L) rather than in a gap.

Authors: We thank the referee for this request for a sharper verification. The revised §4 now contains an expanded computation of ‖ℒψ_n‖. After splitting into the free Laplacian contribution (which vanishes by the standard cut-off estimates) and the perturbation terms, the r^{-3} tails of the curvature and Maxwell-field coefficients are integrated against the support of the cut-off derivatives; the resulting bound is O(1/n) and therefore ‖ℒψ_n‖→0. This confirms that the constructed sequence is a Weyl sequence for eigenvalue 0 and places 0 in the essential spectrum. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The derivation establishes essential self-adjointness of the linearized Einstein-Maxwell operator L and the r^{-3} threshold separating relatively compact perturbations from essential spectrum via delocalized zero modes. These steps apply standard analytic perturbation theory and Weyl-sequence constructions directly to the stated decay assumptions on asymptotically flat manifolds, controlling quadratic-form perturbations and identifying sigma_ess contributions without reducing any claimed prediction or uniqueness result to a fitted parameter, self-definition, or load-bearing self-citation. The unification with memory effects and the corroborating finite-difference simulations follow from the spectral analysis rather than presupposing the threshold. The manuscript is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard domain assumptions from spectral theory and asymptotic analysis in general relativity; no free parameters or new entities are introduced in the abstract.

axioms (2)

domain assumption Spacetime manifolds are asymptotically flat with well-defined decay rates at infinity.
Required to define the essential spectrum and relative compactness of perturbations for Laplace-type operators.
domain assumption The linearized Einstein-Maxwell operator is essentially self-adjoint on the chosen function spaces.
Invoked to guarantee real spectrum and to apply perturbation theory for the decay thresholds.

pith-pipeline@v0.9.0 · 5490 in / 1559 out tokens · 76915 ms · 2026-05-17T23:02:59.161511+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We work on a three-dimensional, asymptotically flat Riemannian manifold (Sigma, g(0)) ... |Riem(0)|=O(r^{-3}) ... Theorem 3.3 (Einstein-Maxwell spectral threshold for p >= 3)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

21 extracted references · 21 canonical work pages · 6 internal anchors

[1]

Kato,Perturbation Theory for Linear Operators, 2nd ed

T. Kato,Perturbation Theory for Linear Operators, 2nd ed. (Springer, Berlin, 1976)

work page 1976
[2]

Elliptic Differential Operators on Noncompact Man- ifolds,

R. B. Lockhart and R. C. McOwen, “Elliptic Differential Operators on Noncompact Man- ifolds,”Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)12, 409 (1985)

work page 1985
[3]

Essential self-adjointness of powers of generators of hyperbolic equations,

P. R. Chernoff, “Essential self-adjointness of powers of generators of hyperbolic equations,” J. Funct. Anal.12, 401 (1973)

work page 1973
[4]

R. M. Wald,General Relativity(University of Chicago Press, Chicago, 1984). 17

work page 1984
[5]

The red-shift effect and radiation decay on black hole spacetimes

M. Dafermos and I. Rodnianski, “Decay for solutions of the wave equation on Kerr exterior spacetimes I–II: The cases|a| ≪Mor axisymmetry,”Ann. Math. (2)168, 901 (2008), arXiv:gr-qc/0512119

work page internal anchor Pith review Pith/arXiv arXiv 2008
[6]

Nonlinear nature of gravitation and gravitational-wave experiments,

D. Christodoulou, “Nonlinear nature of gravitation and gravitational-wave experiments,” Phys. Rev. Lett.67, 1486 (1991)

work page 1991
[7]

Symplectic geometry of radiative modes and conserved quantities at null infinity,

A. Ashtekar and M. Streubel, “Symplectic geometry of radiative modes and conserved quantities at null infinity,”Proc. R. Soc. Lond. A376, 585 (1981)

work page 1981
[8]

Gravitational Memory, BMS Supertranslations and Soft Theorems

A. Strominger and A. Zhiboedov, “Gravitational Memory, BMS Supertranslations and Soft Theorems,”J. High Energy Phys.01, 086 (2016), arXiv:1411.5745 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[9]

Lectures on the Infrared Structure of Gravity and Gauge Theory

A. Strominger,Lectures on the Infrared Structure of Gravity and Gauge Theory(Princeton University Press, Princeton, 2017), arXiv:1703.05448 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[10]

Celestial Amplitudes and Asymptotic Symmetries,

A. Strominger and A. Zhiboedov, “Celestial Amplitudes and Asymptotic Symmetries,” Rev. Mod. Phys.93, 045002 (2021), arXiv:2011.01895 [hep-th]

work page arXiv 2021
[11]

An electromagnetic analog of gravitational wave memory

L. Bieri and D. Garfinkle, “An electromagnetic analogue of gravitational wave memory,” Class. Quantum Grav.30, 195009 (2013), arXiv:1307.5098 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2013
[12]

Global aspects of radiation memory

J. Winicour, “Global aspects of electromagnetic memory,”Class. Quantum Grav.31, 205003 (2014), arXiv:1407.0259 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[13]

Color Memory

M. Pate, A. M. Raclariu, and A. Strominger, “Color Memory: A Yang–Mills Analog of Gravitational Wave Memory,”Phys. Rev. Lett.119, 261602 (2017), arXiv:1707.08016 [hep- th]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[14]

Reed and B

M. Reed and B. Simon,Methods of Modern Mathematical Physics, Vol. IV: Analysis of Operators(Academic Press, New York, 1978)

work page 1978
[15]

Electromagnetic Memory Without a Velocity Kick,

A. A. Youssef and D. R. Nichols, “Electromagnetic Memory Without a Velocity Kick,” Phys. Rev. D109, 064018 (2024), arXiv:2311.06325 [gr-qc]

work page arXiv 2024
[16]

GW241011 and GW241110: Exploring Binary Formation and Fundamental Physics with Asymmetric, High-spin Black Hole Coalescences,

A. G. Abacet al.[LIGO–Virgo–KAGRA Collaboration], “GW241011 and GW241110: Exploring Binary Formation and Fundamental Physics with Asymmetric, High-spin Black Hole Coalescences,”Astrophys. J. Lett.993, L21 (2025)

work page 2025
[17]

The gravitational-wave memory effect,

M. Favata, “The gravitational-wave memory effect,”Class. Quantum Grav.26, 175016 (2009)

work page 2009
[18]

Nonlinearities in Black Hole Ringdowns,

K. Mitman, M. Lagos, L. C. Stein, S. Ma, L. Hui, Y. Chen, N. Deppe, F. H´ ebert, L. E. Kidder, J. Moxon, M. A. Scheel, S. A. Teukolsky, W. Throwe, and N. L. Vu, “Nonlinearities in Black Hole Ringdowns,”Phys. Rev. Lett.130, 081402 (2023), doi:10.1103/PhysRevLett.130.081402, arXiv:2208.07380 [gr-qc]

work page doi:10.1103/physrevlett.130.081402 2023
[19]

Gravitational memory in binary black hole mergers,

D. Pollney and C. Reisswig, “Gravitational memory in binary black hole mergers,”Astro- phys. J. Lett.732, L13 (2011). 18

work page 2011
[20]

Wilson, (2025)

M. Wilson, (2025). Curvature Decay and the Spectrum of the Non-Abelian Laplacian on R3. ArXiv. https://arxiv.org/abs/2511.03532 [math-ph], presented at the 2025 TAOAPS Conference; submitted to theJ. Spectr. Theory

work page arXiv 2025
[21]

Wilson, (2025)

M. Wilson, (2025). Ther −3 Curvature Decay and the Infrared Structure of Linearized Gravity. ArXiv. https://arxiv.org/abs/2511.05345 [gr-qc], submitted to Ann. Henri Poincar´ e. 19

work page arXiv 2025

[1] [1]

Kato,Perturbation Theory for Linear Operators, 2nd ed

T. Kato,Perturbation Theory for Linear Operators, 2nd ed. (Springer, Berlin, 1976)

work page 1976

[2] [2]

Elliptic Differential Operators on Noncompact Man- ifolds,

R. B. Lockhart and R. C. McOwen, “Elliptic Differential Operators on Noncompact Man- ifolds,”Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)12, 409 (1985)

work page 1985

[3] [3]

Essential self-adjointness of powers of generators of hyperbolic equations,

P. R. Chernoff, “Essential self-adjointness of powers of generators of hyperbolic equations,” J. Funct. Anal.12, 401 (1973)

work page 1973

[4] [4]

R. M. Wald,General Relativity(University of Chicago Press, Chicago, 1984). 17

work page 1984

[5] [5]

The red-shift effect and radiation decay on black hole spacetimes

M. Dafermos and I. Rodnianski, “Decay for solutions of the wave equation on Kerr exterior spacetimes I–II: The cases|a| ≪Mor axisymmetry,”Ann. Math. (2)168, 901 (2008), arXiv:gr-qc/0512119

work page internal anchor Pith review Pith/arXiv arXiv 2008

[6] [6]

Nonlinear nature of gravitation and gravitational-wave experiments,

D. Christodoulou, “Nonlinear nature of gravitation and gravitational-wave experiments,” Phys. Rev. Lett.67, 1486 (1991)

work page 1991

[7] [7]

Symplectic geometry of radiative modes and conserved quantities at null infinity,

A. Ashtekar and M. Streubel, “Symplectic geometry of radiative modes and conserved quantities at null infinity,”Proc. R. Soc. Lond. A376, 585 (1981)

work page 1981

[8] [8]

Gravitational Memory, BMS Supertranslations and Soft Theorems

A. Strominger and A. Zhiboedov, “Gravitational Memory, BMS Supertranslations and Soft Theorems,”J. High Energy Phys.01, 086 (2016), arXiv:1411.5745 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2016

[9] [9]

Lectures on the Infrared Structure of Gravity and Gauge Theory

A. Strominger,Lectures on the Infrared Structure of Gravity and Gauge Theory(Princeton University Press, Princeton, 2017), arXiv:1703.05448 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2017

[10] [10]

Celestial Amplitudes and Asymptotic Symmetries,

A. Strominger and A. Zhiboedov, “Celestial Amplitudes and Asymptotic Symmetries,” Rev. Mod. Phys.93, 045002 (2021), arXiv:2011.01895 [hep-th]

work page arXiv 2021

[11] [11]

An electromagnetic analog of gravitational wave memory

L. Bieri and D. Garfinkle, “An electromagnetic analogue of gravitational wave memory,” Class. Quantum Grav.30, 195009 (2013), arXiv:1307.5098 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2013

[12] [12]

Global aspects of radiation memory

J. Winicour, “Global aspects of electromagnetic memory,”Class. Quantum Grav.31, 205003 (2014), arXiv:1407.0259 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2014

[13] [13]

Color Memory

M. Pate, A. M. Raclariu, and A. Strominger, “Color Memory: A Yang–Mills Analog of Gravitational Wave Memory,”Phys. Rev. Lett.119, 261602 (2017), arXiv:1707.08016 [hep- th]

work page internal anchor Pith review Pith/arXiv arXiv 2017

[14] [14]

Reed and B

M. Reed and B. Simon,Methods of Modern Mathematical Physics, Vol. IV: Analysis of Operators(Academic Press, New York, 1978)

work page 1978

[15] [15]

Electromagnetic Memory Without a Velocity Kick,

A. A. Youssef and D. R. Nichols, “Electromagnetic Memory Without a Velocity Kick,” Phys. Rev. D109, 064018 (2024), arXiv:2311.06325 [gr-qc]

work page arXiv 2024

[16] [16]

GW241011 and GW241110: Exploring Binary Formation and Fundamental Physics with Asymmetric, High-spin Black Hole Coalescences,

A. G. Abacet al.[LIGO–Virgo–KAGRA Collaboration], “GW241011 and GW241110: Exploring Binary Formation and Fundamental Physics with Asymmetric, High-spin Black Hole Coalescences,”Astrophys. J. Lett.993, L21 (2025)

work page 2025

[17] [17]

The gravitational-wave memory effect,

M. Favata, “The gravitational-wave memory effect,”Class. Quantum Grav.26, 175016 (2009)

work page 2009

[18] [18]

Nonlinearities in Black Hole Ringdowns,

K. Mitman, M. Lagos, L. C. Stein, S. Ma, L. Hui, Y. Chen, N. Deppe, F. H´ ebert, L. E. Kidder, J. Moxon, M. A. Scheel, S. A. Teukolsky, W. Throwe, and N. L. Vu, “Nonlinearities in Black Hole Ringdowns,”Phys. Rev. Lett.130, 081402 (2023), doi:10.1103/PhysRevLett.130.081402, arXiv:2208.07380 [gr-qc]

work page doi:10.1103/physrevlett.130.081402 2023

[19] [19]

Gravitational memory in binary black hole mergers,

D. Pollney and C. Reisswig, “Gravitational memory in binary black hole mergers,”Astro- phys. J. Lett.732, L13 (2011). 18

work page 2011

[20] [20]

Wilson, (2025)

M. Wilson, (2025). Curvature Decay and the Spectrum of the Non-Abelian Laplacian on R3. ArXiv. https://arxiv.org/abs/2511.03532 [math-ph], presented at the 2025 TAOAPS Conference; submitted to theJ. Spectr. Theory

work page arXiv 2025

[21] [21]

Wilson, (2025)

M. Wilson, (2025). Ther −3 Curvature Decay and the Infrared Structure of Linearized Gravity. ArXiv. https://arxiv.org/abs/2511.05345 [gr-qc], submitted to Ann. Henri Poincar´ e. 19

work page arXiv 2025