Log translation invariance of log soft gravitational radiation

Gianni Boschetti; Miguel Campiglia

REVIEW 2 major objections 3 minor 69 references

Log translation invariance of log soft gravitational radiation

T0 review · 2 major / 3 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read The paper shows that the two universal logarithmic terms in the low-frequency gravitational waveform are invariant under logarithmic translations, explaining the cancellation of outgoing massless contributions and constraining…

desk verdict A useful, honest reorganization of the log soft graviton terms, but the advertised explanation of the massless cancellation rests on a global log-translation identification that is deferred to a companion paper. read the letter →

arxiv 2508.17919 v1 pith:U2GO6APK submitted 2025-08-25 gr-qc hep-th

Gianni Boschetti , Miguel Campiglia This is my paper · ORCID

classification gr-qchep-th MSC 83C30

keywords logsofttheoremslogarithmictranslationsgravitationalradiationgravitontheoremasymptoticsymmetriestimelikeinfinityclassicalscatteringwavetails

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

Gravitational radiation from a classical scattering has a soft-frequency expansion containing two universal logarithmic terms, proportional to $\log\omega$ and $\omega\log^2\omega$. This paper tries to show that those log terms are the shadow of a pure-gauge asymptotic redundancy called logarithmic translation: a shift of asymptotic geodesics by $\log R\,L^\mu$ that does not change the physics. It writes the log soft factors in terms of the log deviation vector $c^\mu$ and verifies $\delta_L h^{(\log)}_{\mu\nu}=0$ and $\delta_L h^{(\log2)}_{\mu\nu}=0$ under a single global log translation acting on both future and past infinity. That invariance explains a previously puzzling cancellation of the outgoing massless-particle contributions, and it yields a recurrence relation that any higher-order log soft term would have to satisfy. The reader should care because it turns an observed coincidence in two perturbative coefficients into a structural symmetry of the asymptotic gravitational field.

What carries the argument

The central object is the log deviation vector $c^\mu$, the coefficient of $\log R$ in an asymptotic trajectory $X^\mu(R)=R V^\mu+\log R\,c^\mu+\cdots$, computed as the limit $c^\mu=\lim_{R\to\infty}\Gamma^\mu_{\nu\rho}X^\nu X^\rho$. Under a logarithmic translation this vector shifts as $\delta_L c^\mu=-L^\mu$. At timelike infinity the same information is carried by the gravitational potential $\sigma$, and for null directions the harmonic log frame gives $c^\mu_{I+}=2G P^\mu_{\mathrm{total}}$, while the radiative log frame sets $c^\mu_{I+}=0$. The argument combines two mechanisms: the phase from soft null-ray drag, $e^{-i\omega\log\omega\, n\cdot c_{I+}}$, and the divergent angular momenta $J^{div}_{i\mu\nu}=c_{i\mu}p_{i\nu}-c_{i\nu}p_{i\mu}$. The load-bearing identities are $\delta_L h^{(1)div}_{\mu\nu}=i L\cdot n\,h^{(0)}_{\mu\nu}$ and $\delta_L h^{(2)div}_{\mu\nu}=i L\cdot n\,h^{(1)div}_{\mu\nu}$, from which $\delta_L h^{(\log)}_{\mu\nu}=0$ and $\delta_L h^{(\log2)}_{\mu\nu}=0$ follow.

What would settle it

Take a two-body scattering process that emits one massless scalar or photon, compute the $\log\omega$ and $\omega\log^2\omega$ waveform coefficients in harmonic gauge and in a gauge related by a nonzero log translation, and check whether the difference vanishes identically. Any residual dependence on the outgoing massless particle's momentum, or any frame dependence of $h^{(\log)}_{\mu\nu}$ or $h^{(\log2)}_{\mu\nu}$, would refute the central claim.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the two known universal log soft factors are not independent accidents but the manifestation of log translation invariance. Writing the soft waveform as $\tilde h_{\mu\nu}$ and using the shortcut in which gravitational drag contributes a phase $e^{-i\omega\log\omega\, n\cdot c_{I+}}$ and particle angular momenta acquire divergent pieces $J^{div}_{i\mu\nu}=c_{i\mu}p_{i\nu}-c_{i\nu}p_{i\mu}$, the log coefficients take the form $h^{(\log)}_{\mu\nu}=-i\,n\cdot c_{I+}h^{(0)}_{\mu\nu}-h^{(1)div}_{\mu\nu}$, with an analogous expression for $h^{(\log2)}_{\mu\nu}$. Under a log translation all deviation vectors shift by the same vector, $\delta_L c^\mu=-L^\mu$, and momentum conservation makes the combination invariant. Because outgoing massless particles have $c_i=c_{I+}$, their net contribution cancels or, in the future radiative log frame $c_{I+}=0$, vanishes term by term; the previously mysterious cancellation is therefore pure gauge. The same logic, applied to the conjectured tower $\omega^{k-1}\log^k\omega$, produces the recurrence $\delta_L a^{(k)}_{\mu\nu}=k(n\cdot L)a^{(k-1)}_{\mu\nu}$ for the coefficients.

Load-bearing premise

The load-bearing premise is that the future and past log translations are the same group, $L^\mu_+=L^\mu_-$, so that outgoing and incoming log deviation vectors shift by the same vector. The invariance check applies that single shift to both sides; if future and past could be shifted independently, the cancellations that leave the soft factors unchanged would not go through.

Editorial extensions

If this is right

The two known universal log terms $h^{(\log)}_{\mu\nu}$ and $h^{(\log2)}_{\mu\nu}$ can be evaluated in any log frame; in the future radiative frame the outgoing massless contributions vanish term by term, not only in total.
The cancellation observed in earlier derivations is reinterpreted as a gauge artifact: in the harmonic log frame it is a conspiracy between the drag phase and the divergent angular momenta, while in the radiative frame it is manifest.
Any prospective higher-order leading-log coefficient of the form $\omega^{k-1}\log^k\omega$ that admits a log-frame expression must satisfy the recurrence $\delta_L a^{(k)}_{\mu\nu}=k(n\cdot L)a^{(k-1)}_{\mu\nu}$, which turns into a polynomial constraint on the undetermined remainders $r^{(k)}_{\mu\nu}$.
The harmonic log frame supplies the relation $c^\mu_{I+}=2G P^\mu_{\mathrm{total}}$, and the global frame identification yields $c^\mu_{I+}+c^\mu_{I-}=0$, connecting the soft theorem derivation to the asymptotic geometry of timelike infinity.

Reading between the lines

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

If the future/past identification survives the companion paper's matching argument, log translations should behave like ordinary translations with an identically vanishing charge: a pure-gauge symmetry that nevertheless constrains radiative data. The paper does not establish the charge interpretation.
The same log-frame logic may apply to log soft photon theorems and to loop-level quantum soft graviton corrections, where a harmonic log frame would again produce deviation vectors proportional to total momentum and outgoing massless contributions could become removable by a log translation.
The recurrence (5.6) could be used as a prediction generator: imposing it on proposed higher-order remainders would fix the first unknown coefficient $r^{(3)}_{\mu\nu}$ up to log-translation-invariant data, providing a concrete test of the symmetry at order $\omega^2\log^3\omega$.
A numerical relativity simulation of a binary system with a massless scalar or photon field could test frame independence directly: extract the $\log\omega$ and $\omega\log^2\omega$ waveform coefficients in coordinates related by a nonzero log translation and check that they remain exactly unchanged.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: the paper reorganizes the two known log soft graviton terms around log translations and shows, cleanly, why the outgoing massless contributions cancel. The rewriting is new and the invariance check is explicit and correct as far as it goes. But the argument leans on a global identification of future and past log translations, Eq. (3.59), that is not established here: the matching is deferred to companion paper [29], and the paper's own Appendix A.2 shows harmonic gauge actually kills log translations. Keep that caveat in mind before citing the explanation as settled.

What is genuinely good: the paper doesn't just restate prior results. Defining log deviation vectors and writing h^(log), h^(log2) through them gives a manifestly invariant form; the check (4.14) is direct. The explanation of the massless cancellation — that in the harmonic frame the massless deviation vectors coincide with c_I^+ and the log translation removes them — is the cleanest I've seen. The recurrence (5.7) for higher-order remainders is a useful constraint, though it is conditional on the remainders admitting log-frame expressions, which the paper says openly is not established. The input soft factors come from earlier work [4,5]; no circularity. The computations are careful and the limitations are stated.

The soft spot is load-bearing. All of Sec. 4 applies the same shift -L to outgoing and incoming deviation vectors. That is legitimate only if L_+=L_-. The paper says this 'arises naturally' in harmonic coordinates, but Appendix A.2 shows the harmonic gauge residual diffeo parameter l must vanish. So one coordinate patch actually freezes log translations; the identification is a nontrivial matching condition across infinity, not a gauge triviality. The authors defer this to [29]. Until that matching argument appears, the invariance proof is conditional, and the stress-test algebra shows that with independent L_+ and L_- the cancellations in (4.13) do not go through. This is the difference between a suggestive explanation and a proven one. The paper would not collapse if Eqs. (4.10)-(4.14) are read as an identity within a fixed global log frame; that reading is fine. But the advertised explanation of the puzzling cancellation needs the global identification.

Who is it for: people working on soft theorems, tails, and infrared structure. It deserves a serious referee: the question is important, the paper is honest about what is missing, and the conditional statement is already worth having. A referee should push on (3.59) and on the existence assumption behind (5.7). If [29] delivers the matching, this becomes an accepted part of the literature; if not, it remains a well-marked conjecture.

Referee Report

2 major / 3 minor

Summary. This paper studies the two known universal logarithmic terms in the low-frequency expansion of classical gravitational radiation and proposes that they are invariant under logarithmic translations. The authors introduce the log deviation vector c^mu, relate it to the gravitational potential at timelike infinity, and discuss harmonic and radiative log frames. They argue that future and past log translations should be identified, Eq. (3.59), yielding a single global log translation group. Using the heuristic derivation of the log soft factors from [4,5], they express h^(log) and h^(log2) in terms of c^mu and verify their invariance under the log translation action, thereby offering an explanation for the cancellation of outgoing massless contributions. They then derive a recurrence relation for higher-order log soft remainders. The paper is explicitly presented as preparatory to a companion paper [29] that will provide a fully asymptotic derivation.

Significance. If the main claim holds, the paper gives a simple structural explanation for a puzzling cancellation that had only been observed in the first two universal log terms, and it provides a consistency condition for conjectured higher-order terms. The invariance computations in Section 4 are explicit, and the expressions reproduce the rigorously derived log soft factors of [4,5]. The paper is also honest about the conditional status of the higher-order discussion in Section 5. The overall significance is real but conditional: the invariance proof rests on the global identification of future and past log translations, which is deferred to a companion paper. If that matching condition is established, the paper will be a valuable contribution to the asymptotic-symmetry understanding of log soft theorems.

major comments (2)

[Section 3.5, Eq. (3.59)] The identification L_+ = L_- is the load-bearing input for the invariance proof. In Section 4, Eq. (4.12) applies the same shift -L^mu to c_I+ and to every hard-particle deviation vector, and the cancellations leading to Eq. (4.14) rely on this common shift together with momentum conservation. If future and past log translations were independent, a direct variation of Eq. (4.10) would leave uncancelled terms proportional to P^mu_total (L_+-L_-)^nu and to ((L_+-L_-)·n) times incoming-particle sums, neither of which vanishes for L_+ ≠ L_-. The paper states that Eq. (3.59) arises naturally in harmonic coordinates or follows from matching at infinity deferred to [29]. However, Appendix A.2, Eqs. (A.40)-(A.41), shows that the residual harmonic-gauge log translation parameter l must vanish, so a single harmonic coordinate patch does not by itself deliver the nontrivial global identification. The central claim of log soft factor invariance is therefore conditional on an unproved global-matching result. Please either prove Eq. (3.59) in this paper or state it explicitly as an assumption and revise the claims in the abstract and Section 4 accordingly.
[Footnote 15 and Eq. (4.13)] The second invariance relation in Eq. (4.13) uses sum_i J^div_iμν = 0, and the footnote strengthens this to the statement that incoming and outgoing divergent angular momenta vanish separately. This is a necessary step for the claimed invariance of h^(log2) in Eq. (4.14). No proof or reference is supplied for this fact. Please provide a derivation, for example from the explicit expression for c_i^mu indicated in footnote 17, or cite a precise result. Without this, the log2 invariance statement is not fully supported as written.

minor comments (3)

[Abstract and Section 5] The abstract says the work 'leads to a recurrence relation' for higher-order universal log soft terms, but Section 5 explicitly states that the recurrence is conditional on the existence of log-frame expressions for the undetermined remainders and that the proposal of [12] cannot be checked. Please qualify the abstract wording to reflect this conditionality.
[Reference [29]] Reference [29] is the companion paper that is supposed to supply the proof of the global matching condition and the fully asymptotic derivation. It is cited without a preprint number or a citable source. Since Eq. (3.59) is load-bearing, either the proof should appear here or the companion paper should be made available.
[Appendix A.2, after Eq. (A.47)] The text uses 'Ecs.' where 'Eqs.' is intended; please correct this typographical issue.

Circularity Check

1 steps flagged · score 4.0 of 10

Invariance algebra is self-contained, but the global identification L_+ = L_- (Eq. 3.59) is load-bearing and deferred to the authors' own companion paper [29].

self citation load bearing [Section 3.5, Eq. (3.59); used in Section 4, Eqs. (4.12)-(4.14)]
"these two transformations should not be regarded as independent, but instead satisfy L^μ_+ = L^μ_−. ... Alternatively, as discussed in [29], it follows from the matching properties of the gravitational field across timelike, null and spatial infinity. ... Under a log translation, both the 'soft' null-ray deviation vector in (4.5) and the 'hard' particles' deviation vector in (4.7) transform according to (3.60) δ_L c^μ_{I+} = δ_L c^μ_i = −L^μ."

The invariance check (4.14) is a direct calculation using (4.12), which assumes one common L for future and past data. If L_+ and L_- were independent, the variations (4.13) would retain terms proportional to (L_+-L_-) times total momentum or incoming-particle sums, so the cancellations would fail. The paper's support for (3.59) is a one-sentence appeal to harmonic coordinates—despite Appendix A.2 concluding that the harmonic-gauge residual log-translation parameter l must vanish—or a deferral to the same authors' companion paper [29]. Hence the central claim is conditional on an unproved, self-cited matching condition.

full rationale

The log soft factors are not derived in this paper; they are taken from independent prior computations [1-6], and the invariance proof reduces to momentum conservation and the vanishing of total divergent angular momentum, so the central algebra is not a fit or a definitional tautology. The explanation of the outgoing-massless cancellation via the radiative log frame is structurally sound. However, the proof applies a single log-translation parameter to both future and past (3.59)-(3.60), and the paper's only justifications for this identification are a brief harmonic-coordinate remark and a reference to the authors' own companion paper [29]. If future and past log translations were independent, the cancellations in (4.13) would not go through. This makes the headline invariance result conditional on an unproved, self-cited matching assumption, warranting a moderate circularity score rather than a clean 0-2.

Assumptions & free parameters 1 free parameters · 7 assumptions · 0 invented entities

The paper fits no data. The only hand-chosen parameter is lambda in the Green's function (3.19), which defines a log frame; the central claim is invariance under the corresponding log translations. The main unproved input is the identity L_+ = L_-, followed by the standard asymptotic-flatness assumptions and the heuristic shortcut inherited from the soft-theorem literature.

free parameters (1)

lambda (Green's function integration constant) = lambda = -2 for radiative log frame, lambda = 0 in harmonic gauge; otherwise arbitrary
Appears in G_lambda in Eq. (3.19). Not fitted to data; it defines the log frame. The central claim is that physical log soft factors are independent of lambda, so this parameter is a gauge choice rather than a hidden fit.

assumptions (7)

domain assumption Asymptotic flatness: g_mu nu = eta_mu nu + (1/tau) gamma_mu nu + ..., and asymptotic timelike geodesics X^mu = tau V^mu + log tau c^mu + ... (Eqs. (2.3), (3.4)).
Defines the timelike-infinity framework and the log deviation vector; standard in the asymptotic-flatness literature but an input, not derived here.
domain assumption Leading Einstein equations reduce to (D^2 - 3) sigma = 4 pi G rho with a one-parameter Green's function G_lambda (Eqs. (3.16)-(3.19)).
The one-parameter family of Green's functions is an input whose parameter lambda is later tied to the log frame.
ad hoc to paper Future and past logarithmic translations are identified: L_+ = L_- (Eq. (3.59)).
Load-bearing: the invariance proof in Sec. 4 uses a single shift for both in and out particles. The paper argues from harmonic coordinates and defers the matching proof to [29].
domain assumption For asymptotically null trajectories the log deviation vector is direction-independent and in harmonic gauge equals c_I = 2G P_total (Eqs. (3.40), (3.56)).
Reproduces Eq. (3.29) of [3]; it is the harmonic-frame input that makes the massless cancellation manifest in that frame.
ad hoc to paper The total divergent angular momentum of incoming and outgoing particles vanishes separately (footnote 15).
Used in the second transformation in (4.13); asserted without detailed derivation in the text.
domain assumption The O(G) tree-level waveform obeys the all-order expansion (5.1)-(5.2), and the replacement b_i -> -log omega c_i captures the leading-log sector (from [46,47] and [5,12]).
Basis for extending the invariance analysis to higher log orders; the remainder structure is not proven, as the paper acknowledges.
domain assumption The asymptotic magnetic Weyl curvature vanishes, B_ab = 0 (A.24).
Standard condition on physical scattering spacetimes; verified for the harmonic-gauge metric (3.33) in appendix A.2.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Log translation invariance of log soft gravitational radiation." pith.science (2026). https://pith.science/paper/U2GO6APK

@misc{pith2026250817919,
  author       = {Pith},
  title        = {Pith review of: Log translation invariance of log soft gravitational radiation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/U2GO6APK}},
  note         = {Machine review of arXiv:2508.17919}
}

read the original abstract

The gravitational radiation emitted during a classical scattering process is known to exhibit two universal logarithmic terms in its soft frequency expansion. We show that these terms can be written in a way that makes the action of \emph{logarithmic translations} manifest. Invariance under log translations naturally explains a puzzling cancellation in the contribution from outgoing massless particles and leads to a recurrence relation for expected higher-order universal log soft terms.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

69 extracted references · 61 canonical work pages

[29]

An asymptotic proof of the classica l log soft graviton theorem

G. Boschetti, M. Campiglia, “An asymptotic proof of the classica l log soft graviton theorem”

work page
[1]

Logarithmic Terms in the Soft Expansion in Four Dimensions,

A. Laddha and A. Sen, “Logarithmic Terms in the Soft Expansion in Four Dimensions,” JHEP 10, 056 (2018)

work page 2018
[2]

Observational Signature of the Logarit hmic Terms in the Soft Graviton Theorem,

A. Laddha and A. Sen, “Observational Signature of the Logarit hmic Terms in the Soft Graviton Theorem,” Phys. Rev. D 100, no.2, 024009 (2019)

work page 2019
[3]

Classical and Quantum Results on Logarith mic Terms in the Soft Theorem in Four Dimensions,

B. Sahoo and A. Sen, “Classical and Quantum Results on Logarith mic Terms in the Soft Theorem in Four Dimensions,” JHEP 02, 086 (2019)

work page 2019
[4]

Proof of the classical soft gr aviton theorem in D = 4,

A. P. Saha, B. Sahoo and A. Sen, “Proof of the classical soft gr aviton theorem in D = 4,” JHEP 06, 153 (2020)

work page 2020
[5]

Classical Sub-subleading Soft Photon and Soft Grav iton Theorems in Four Spacetime Dimensions,

B. Sahoo, “Classical Sub-subleading Soft Photon and Soft Grav iton Theorems in Four Spacetime Dimensions,” JHEP 12, 070 (2020)

work page 2020
[6]

Classical soft graviton theorem rewritte n,

B. Sahoo and A. Sen, “Classical soft graviton theorem rewritte n,” JHEP 01, 077 (2022)

work page 2022
[7]

Gravitational Wave Tails from Soft Theorem: A Short Re view,

A. Sen, “Gravitational Wave Tails from Soft Theorem: A Short Re view,” [arXiv:2408.08851 [hep-th]]

arXiv

Show all 69 references

[8]

Logarithmic soft graviton theorems from superrotation Ward identities,

S. Agrawal, L. Donnay, K. Nguyen and R. Ruzziconi, “Logarithmic soft graviton theorems from superrotation Ward identities,” [arXiv:2309.11220 [hep-th]]

arXiv
[9]

Asymptotic Symmetries for Log arithmic Soft Theorems in Gauge Theory and Gravity,

S. Choi, A. Laddha and A. Puhm, “Asymptotic Symmetries for Log arithmic Soft Theorems in Gauge Theory and Gravity,” [arXiv:2403.13053 [hep-th]]

arXiv
[10]

The classical super-rotation infrared triangle. Classical logarithmic soft theorem as conservation law in gravity,

S. Choi, A. Laddha and A. Puhm, “The classical super-rotation infrared triangle. Classical logarithmic soft theorem as conservation law in gravity,” JHEP 04, 138 (2025)

2025
[11]

Lectures on the Infrared Structure of Gra vity and Gauge Theory,

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

arXiv
[12]

Logarithmic soft theorems and soft spectra,

F. Alessio, P. Di Vecchia and C. Heissenberg, “Logarithmic soft theorems and soft spectra,” JHEP 11, 124 (2024)

2024
[13]

’Gauge-Invariant’ Variables in General Relat ivity,

P. G. Bergmann, “’Gauge-Invariant’ Variables in General Relat ivity,” Phys. Rev. 124, 274-278 (1961)

1961
[14]

Logarithmic ambiguities in the description of spat ial inﬁnity

A. Ashtekar, “Logarithmic ambiguities in the description of spat ial inﬁnity”, Found Phys 15, 419–431 (1985) – 25 –

1985
[15]

Einstein’s equations near spatial inﬁn ity,

R. Beig and B. G. Schmidt, “Einstein’s equations near spatial inﬁn ity,” Commun. Math. Phys. 87, no.1, 65-80 (1982)

1982
[16]

Logarithmic supertranslations and supertranslation-invariant Lorentz charges,

O. Fuentealba, M. Henneaux and C. Troessaert, “Logarithmic supertranslations and supertranslation-invariant Lorentz charges,” JHEP 02, 248 (2023)

2023
[17]

Log supertr anslations at Spatial Inﬁnity,

S. Mishra, K. Banerjee and J. Bhattacharyya, “Log supertr anslations at Spatial Inﬁnity,” [arXiv:2504.19910 [gr-qc]]
[18]

On supertran slation invariant Lorentz charges,

S. Chakraborty, S. K. J. Hoque and A. Virmani, “On supertran slation invariant Lorentz charges,” Gen. Rel. Grav. 57, no.2, 44 (2025)

2025
[19]

A uniﬁed treatment of null and spatial inﬁnity in general relativity. I - Universal structure, asymptotic symmetries, and c onserved quantities at spatial inﬁnity,

A. Ashtekar and R. O. Hansen, “A uniﬁed treatment of null and spatial inﬁnity in general relativity. I - Universal structure, asymptotic symmetries, and c onserved quantities at spatial inﬁnity,” J. Math. Phys. 19, 1542-1566 (1978)

1978
[20]

Asymptotic Structure of the Gravitational Fie ld at Spatial Inﬁnity

A. Ashtekar, “Asymptotic Structure of the Gravitational Fie ld at Spatial Inﬁnity”, in: General Relativity and Gravitation: One Hundred Years After the b irth of Albert Einstein, edited by A. Held, (Plenum, New York, 1980)

1980
[21]

Spatial inﬁnity as a boundary o f space-time,

A. Ashtekar and J. D. Romano, “Spatial inﬁnity as a boundary o f space-time,” Class. Quant. Grav. 9, 1069-1100 (1992)

1992
[22]

An asymptotic framework for gravitational scattering,

G. Comp` ere, S. E. Gralla and H. Wei, “An asymptotic framework for gravitational scattering,” Class. Quant. Grav. 40, no.20, 205018 (2023)

2023
[23]

Timelike inﬁnity,

S. Persides, “Timelike inﬁnity,” J. Math. Phys. 23, no.2, 283-288 (1982)

1982
[24]

Properties of spacetimes that are asymptotically ﬂ at at timelike inﬁnity

C. Cutler, “Properties of spacetimes that are asymptotically ﬂ at at timelike inﬁnity”, Class. Quant. Grav. 6, no.8, 1075 (1989)

1989
[25]

Timelike inﬁnity and asymptotic symmetr y,

U. Gen and T. Shiromizu, “Timelike inﬁnity and asymptotic symmetr y,” J. Math. Phys. 39, 6573-6592 (1998)

1998
[26]

Asymptotic symmetries of gravity a nd soft theorems for massive particles,

M. Campiglia and A. Laddha, “Asymptotic symmetries of gravity a nd soft theorems for massive particles,” JHEP 12, 094 (2015)

2015
[27]

Supertranslations at timelike inﬁnity,

S. Chakraborty, D. Ghosh, S. J. Hoque, A. Khairnar and A. Vir mani, “Supertranslations at timelike inﬁnity,” JHEP 02, 022 (2022)

2022
[28]

Car rollian and celestial spaces at inﬁnity,

J. Figueroa-O’Farrill, E. Have, S. Prohazka and J. Salzer, “Car rollian and celestial spaces at inﬁnity,” JHEP 09, 007 (2022)

2022
[30]

Gravitat ional waves in general relativity. 7. Waves from axisymmetric isolated systems,

H. Bondi, M. G. J. van der Burg and A. W. K. Metzner, “Gravitat ional waves in general relativity. 7. Waves from axisymmetric isolated systems,” Proc. Roy . Soc. Lond. A 269, 21 (1962)

1962
[31]

Gravitational waves in general relativity. 8. Wav es in asymptotically ﬂat space-times,

R. K. Sachs, “Gravitational waves in general relativity. 8. Wav es in asymptotically ﬂat space-times,” Proc. Roy. Soc. Lond. A 270, 103 (1962)

1962
[32]

A Class of Null Flat-Space Coord inate Systems,

E. T. Newman and T. W. J. Unti, “A Class of Null Flat-Space Coord inate Systems,” J. Math. Phys. 4, no.12, 1467-1469 (1963)

1963
[33]

Radiative gravitational ﬁelds in general relativity . 2. Asymptotic behaviour at future null inﬁnity,

L. Blanchet, “Radiative gravitational ﬁelds in general relativity . 2. Asymptotic behaviour at future null inﬁnity,” Proc. Roy. Soc. Lond. A 409, 383-399 (1987)

1987
[34]

Gravitational radiation from postNewtonian sou rces and inspiraling compact binaries,

L. Blanchet, “Gravitational radiation from postNewtonian sou rces and inspiraling compact binaries,” Living Rev. Rel. 5, 3 (2002) – 26 –

2002
[35]

Celestial IR divergences and the eﬀe ctive action of supertranslation modes,

K. Nguyen and J. Salzer, “Celestial IR divergences and the eﬀe ctive action of supertranslation modes,” JHEP 09, 144 (2021)

2021
[36]

Loop Corrected Soft Photon Theo rem as a Ward Identity,

M. Campiglia and A. Laddha, “Loop Corrected Soft Photon Theo rem as a Ward Identity,” JHEP 10, 287 (2019)

2019
[37]

Mass Positivity from Focussing a nd the Structure of io

A. Ashtekar and R. Penrose, “Mass Positivity from Focussing a nd the Structure of io ”, Twistor Newsletter, 31 (1991)

1991
[38]

Infrared photons and gravitons,

S. Weinberg, “Infrared photons and gravitons,” Phys. Rev. 140, B516-B524 (1965)

1965
[39]

Gravitational Memory, BMS S upertranslations and Soft Theorems,

A. Strominger and A. Zhiboedov, “Gravitational Memory, BMS S upertranslations and Soft Theorems,” JHEP 01, 086 (2016)

2016
[40]

Spin-dependent gravitational tail me mory in D = 4,

D. Ghosh and B. Sahoo, “Spin-dependent gravitational tail me mory in D = 4,” Phys. Rev. D 105, no.2, 025024 (2022)

2022
[41]

On the classical limit of the (sub) n-leading soft graviton theorems in D = 4 without deﬂection,

S. Akhtar, “On the classical limit of the (sub) n-leading soft graviton theorems in D = 4 without deﬂection,” JHEP 12, 207 (2024)

2024
[42]

Classical proof of the classical soft gr aviton theorem in D >4,

A. Laddha and A. Sen, “Classical proof of the classical soft gr aviton theorem in D >4,” Phys. Rev. D 101, no.8, 084011 (2020)

2020
[43]

Gravity Waves from Soft Theorem in Gen eral Dimensions,

A. Laddha and A. Sen, “Gravity Waves from Soft Theorem in Gen eral Dimensions,” JHEP 09, 105 (2018)

2018
[44]

Sub-subleading Soft Graviton Theorem in Generic Theories of Quantum Gravity,

A. Laddha and A. Sen, “Sub-subleading Soft Graviton Theorem in Generic Theories of Quantum Gravity,” JHEP 10, 065 (2017)

2017
[45]

Evidence for a New Soft Gravit on Theorem,

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

arXiv
[46]

Inﬁnite Set of Soft Theorems in Gauge- Gravity Theories as Ward-Takahashi Identities,

Y. Hamada and G. Shiu, “Inﬁnite Set of Soft Theorems in Gauge- Gravity Theories as Ward-Takahashi Identities,” Phys. Rev. Lett. 120, no.20, 201601 (2018)

2018
[47]

Inﬁnite Soft Theorems from Gauge Symmetry,

Z. Z. Li, H. H. Lin and S. Q. Zhang, “Inﬁnite Soft Theorems from Gauge Symmetry,” Phys. Rev. D 98, no.4, 045004 (2018)

2018
[48]

On BMS Invariance of Gravitational Scatterin g,

A. Strominger, “On BMS Invariance of Gravitational Scatterin g,” JHEP 07, 152 (2014)

2014
[49]

Holograph ic symmetry algebras for gauge theory and gravity,

A. Guevara, E. Himwich, M. Pate and A. Strominger, “Holograph ic symmetry algebras for gauge theory and gravity,” JHEP 11, 152 (2021)

2021
[50]

w1+∞ Algebra and the Celestial Sphere: Inﬁnite Towers of Soft Graviton , Photon, and Gluon Symmetries,

A. Strominger, “ w1+∞ Algebra and the Celestial Sphere: Inﬁnite Towers of Soft Graviton , Photon, and Gluon Symmetries,” Phys. Rev. Lett. 127, no.22, 221601 (2021)

2021
[51]

Higher spin dynamic s in gravity and w1+ ∞ celestial symmetries,

L. Freidel, D. Pranzetti and A. M. Raclariu, “Higher spin dynamic s in gravity and w1+ ∞ celestial symmetries,” Phys. Rev. D 106, no.8, 086013 (2022)

2022
[52]

Celestial w1+∞ charges and the subleading structure of asymptotically-ﬂat spacetimes,

M. Geiller, “Celestial w1+∞ charges and the subleading structure of asymptotically-ﬂat spacetimes,” SciPost Phys. 18, no.1, 023 (2025)

2025
[53]

Asymptotic higher spin symmetries I: covariant wedge algebra in gravity,

N. Cresto and L. Freidel, “Asymptotic higher spin symmetries I: covariant wedge algebra in gravity,” Lett. Math. Phys. 115, no.2, 39 (2025)

2025
[54]

Asymptotic Higher Spin Symmetries II : Noether Realization in Gravity,

N. Cresto and L. Freidel, “Asymptotic Higher Spin Symmetries II : Noether Realization in Gravity,” [arXiv:2410.15219 [hep-th]]
[55]

On Loop Corrections to Sublea ding Soft Behavior of Gluons and Gravitons,

Z. Bern, S. Davies and J. Nohle, “On Loop Corrections to Sublea ding Soft Behavior of Gluons and Gravitons,” Phys. Rev. D 90, no.8, 085015 (2014) – 27 –

2014
[56]

Loop Corrections to Soft Theo rems in Gauge Theories and Gravity,

S. He, Y. t. Huang and C. Wen, “Loop Corrections to Soft Theo rems in Gauge Theories and Gravity,” JHEP 12, 115 (2014)

2014
[57]

Universality of loop corrected soft t heorems in 4d,

H. Krishna and B. Sahoo, “Universality of loop corrected soft t heorems in 4d,” JHEP 11, 233 (2023)

2023
[58]

Holography in the ﬂat space limit,

L. Susskind, “Holography in the ﬂat space limit,” AIP Conf. Proc. 493, no.1, 98-112 (1999)

1999
[59]

A Holographic reduction of Mink owski space-time,

J. de Boer and S. N. Solodukhin, “A Holographic reduction of Mink owski space-time,” Nucl. Phys. B 665, 545-593 (2003)

2003
[60]

Asymptotic ﬂatness, little string theory, and holog raphy,

D. Marolf, “Asymptotic ﬂatness, little string theory, and holog raphy,” JHEP 03, 122 (2007)

2007
[61]

Symmetries of asymptotically ﬂ at 4 dimensional spacetimes at null inﬁnity revisited,

G. Barnich and C. Troessaert, “Symmetries of asymptotically ﬂ at 4 dimensional spacetimes at null inﬁnity revisited,” Phys. Rev. Lett. 105, 111103 (2010)

2010
[62]

The Ho lographic Nature of Null Inﬁnity,

A. Laddha, S. G. Prabhu, S. Raju and P. Shrivastava, “The Ho lographic Nature of Null Inﬁnity,” SciPost Phys. 10, no.2, 041 (2021) [arXiv:2002.02448 [hep-th]]

2021 arXiv
[63]

Lectures on Celestial Holography,

A. M. Raclariu, “Lectures on Celestial Holography,” [arXiv:2107.0 2075 [hep-th]]
[64]

Holography in ﬂat spacet imes: the case for Carroll,

A. Bagchi, P. Dhivakar and S. Dutta, “Holography in ﬂat spacet imes: the case for Carroll,” JHEP 08, 144 (2024)

2024
[65]

Decorating Asymptotically Flat Space-Time with the Mod uli Space of String Theory,

A. Sen, “Decorating Asymptotically Flat Space-Time with the Mod uli Space of String Theory,” [arXiv:2506.13876 [hep-th]]

arXiv
[66]

Relaxing the Parity Conditions of Asymptotically Flat Gravity,

G. Comp` ere and F. Dehouck, “Relaxing the Parity Conditions of Asymptotically Flat Gravity,” Class. Quant. Grav. 28, 245016 (2011) [erratum: Class. Quant. Grav. 30, 039501 (2013)]

2011
[67]

Role of Surface Integrals in the Ham iltonian Formulation of General Relativity,

T. Regge and C. Teitelboim, “Role of Surface Integrals in the Ham iltonian Formulation of General Relativity,” Annals Phys. 88, 286 (1974)

1974
[68]

The BMS4 algebra at spatial inﬁnity,

C. Troessaert, “The BMS4 algebra at spatial inﬁnity,” Class. Qu ant. Grav. 35, no.7, 074003 (2018)

2018
[69]

Can scalars have asymptot ic symmetries?,

M. Campiglia, L. Coito and S. Mizera, “Can scalars have asymptot ic symmetries?,” Phys. Rev. D 97, no.4, 046002 (2018) – 28 –

2018

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [29]

An asymptotic proof of the classica l log soft graviton theorem

G. Boschetti, M. Campiglia, “An asymptotic proof of the classica l log soft graviton theorem”

work page

[2] [1]

Logarithmic Terms in the Soft Expansion in Four Dimensions,

A. Laddha and A. Sen, “Logarithmic Terms in the Soft Expansion in Four Dimensions,” JHEP 10, 056 (2018)

work page 2018

[3] [2]

Observational Signature of the Logarit hmic Terms in the Soft Graviton Theorem,

A. Laddha and A. Sen, “Observational Signature of the Logarit hmic Terms in the Soft Graviton Theorem,” Phys. Rev. D 100, no.2, 024009 (2019)

work page 2019

[4] [3]

Classical and Quantum Results on Logarith mic Terms in the Soft Theorem in Four Dimensions,

B. Sahoo and A. Sen, “Classical and Quantum Results on Logarith mic Terms in the Soft Theorem in Four Dimensions,” JHEP 02, 086 (2019)

work page 2019

[5] [4]

Proof of the classical soft gr aviton theorem in D = 4,

A. P. Saha, B. Sahoo and A. Sen, “Proof of the classical soft gr aviton theorem in D = 4,” JHEP 06, 153 (2020)

work page 2020

[6] [5]

Classical Sub-subleading Soft Photon and Soft Grav iton Theorems in Four Spacetime Dimensions,

B. Sahoo, “Classical Sub-subleading Soft Photon and Soft Grav iton Theorems in Four Spacetime Dimensions,” JHEP 12, 070 (2020)

work page 2020

[7] [6]

Classical soft graviton theorem rewritte n,

B. Sahoo and A. Sen, “Classical soft graviton theorem rewritte n,” JHEP 01, 077 (2022)

work page 2022

[8] [7]

Gravitational Wave Tails from Soft Theorem: A Short Re view,

A. Sen, “Gravitational Wave Tails from Soft Theorem: A Short Re view,” [arXiv:2408.08851 [hep-th]]

arXiv