Dual gravitational charges and soft theorems

C.N. Pope; Hadi Godazgar; Mahdi Godazgar

REVIEW 4 major objections 4 minor 6 cited by

Dual gravitational charges and soft theorems

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read The paper argues that dual gravitational NUT charges belong in the phase space of asymptotically flat gravity and, assuming a quantum conservation law, imply a new soft NUT/graviton theorem.

desk verdict A clean phase-space computation and a genuinely useful reworking of asymptotic charges, but the advertised soft NUT theorem is a conjecture resting on a charge normalization the authors themselves leave unresolved. read the letter →

arxiv 1908.01164 v2 pith:ELFBDMAJ submitted 2019-08-03 hep-th gr-qc

Hadi Godazgar , Mahdi Godazgar , C.N. Pope This is my paper · ORCID

classification hep-thgr-qc PACS 04.20.-q04.20.Ha

keywords dualgravitationalchargesNUTchargesofttheoremsBMSsupertranslationsnullinfinityasymptoticflatnessmagneticmonopolesWardidentity

open problems Quantum Gravity

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

Gravity, like electromagnetism, appears to have a magnetic side: the NUT charge, sourced by dual gravitational charges. This paper argues that these charges belong in the phase space of asymptotically flat gravity, and that including them eliminates the need for a boundary condition at spacelike infinity that had previously excluded NUT charge. The argument runs through a complexified supertranslation charge that acts as a time translation on one radiative mode and a supertranslation on the other. If the quantum conservation law for this charge holds, the paper derives a new soft theorem for NUT-charged graviton scattering—the gravitational analogue of the magnetic soft photon theorem. If correct, NUT-charged spacetimes are not pathologies but legitimate scattering backgrounds, and the infrared structure of gravity encodes both electric and magnetic gravitational charge.

What carries the argument

The machinery is the complexified supertranslation charge $\mathcal{Q}_0 = Q_0^{\rm(int)} - i\widetilde{Q}_0^{\rm(int)}$, formed from the usual supertranslation charge and a dual charge built with the Levi-Civita tensor on the two-sphere. This object packages the electric and magnetic gravitational charges as one complex charge, and its Dirac brackets with the radiative modes are what convert the classical phase-space computation into a Ward identity. The non-regularity of Bondi coefficients on the sphere is also load-bearing, because it makes previously discarded total-derivative terms contribute to the charges.

What would settle it

Compute, in a concrete low-energy quantum gravity model, the leading soft-graviton emission factor for initial and final states with definite NUT charge $\tilde E$, and compare it with the factorisation predicted by equations (4.19)–(4.20) with $s(w)=1/(z-w)$. A mismatch, or a first-principles demonstration that $Q_+ S - S Q_- \neq 0$, would refute the claimed soft NUT/graviton theorem.

Watch

Extended reading notes

Core claim

The central claim is that the phase space of radiating gravitational modes can consistently carry dual (NUT) charges once asymptotic flatness is generalised to allow Bondi metric coefficients that are not regular on the two-sphere. With that generalisation, total-derivative terms that earlier derivations discarded become physical, and the revised complexified supertranslation charge $\mathcal{Q}_0 = Q_0^{\rm(int)} - i\widetilde{Q}_0^{\rm(int)}$ acts on radiative modes as $\{\mathcal{Q}_+, C_{zz}\} = s\,\partial_u C_{zz}$ and $\{\mathcal{Q}_+, C_{\bar z\bar z}\} = s\,\partial_u C_{\bar z\bar z} - 2D_{\bar z}^2 s$: a time translation on one mode and a supertranslation on the other, with no boundary condition at spacelike infinity. Assuming conservation of this charge in the quantum theory, the resulting Ward identity is a new soft NUT/graviton theorem, with soft factors carried by states carrying both energy and NUT charge.

Load-bearing premise

The entire soft theorem rests on the unproven quantum conservation law $Q_+ S - S Q_- = 0$ and on the assumed action of the charge on in- and out-scattering states; if either fails, the classical bracket computation does not produce a soft NUT theorem.

Editorial extensions

If this is right

NUT-charged spacetimes are admissible in the null-infinities scattering framework without a separate boundary condition at spacelike infinity, because the dual charge is carried by non-regular Bondi coefficients on the sphere.
The incorrect action of the supertranslation charge on one radiative mode in earlier treatments is cured by keeping the dual charge rather than restricting the phase space.
Conservation of the complexified charge implies a soft NUT/graviton theorem in which the leading soft factor involves both the energy and the NUT charge of each external state.
The complexified charge unifies the usual and dual supertranslation charges as real and imaginary parts, making the new theorem the gravitational magnetic analogue of the magnetic soft photon theorem.
The revised charge expressions change the global dual charge of Taub-NUT to $-\ell/(2G)$, one half of the dual Komar value, a factor the paper leaves as an open analogue of the Komar factor-of-half puzzle.

Reading between the lines

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

A direct test of the conjecture would be a low-energy quantum gravity calculation of soft graviton emission from NUT-charged external states; the leading soft factor should match the factorisation implied by the Ward identity with $s(w)=1/(z-w)$.
If the soft NUT theorem holds, it suggests a NUT-charge memory effect: passage of a wave pulse carrying dual charge would leave a residual imprint in a gravitational-wave detector, extending ordinary supertranslation memory.
The factor-of-two mismatch between the null-infinities dual charge and the Komar dual integral hints that a boundary term of the Noether-charge type may be missing for dual charges; finding such a term would reconcile the two definitions.
The complexified-charge construction is likely to extend to subleading orders and to superrotations, producing a tower of subleading soft NUT theorems.

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

The phase-space part of this paper is the real meat. The Dirac bracket computation in (3.21)–(3.22) is clean and correct as far as I can tell: the complexified supertranslation charge acts as a time translation on C_zz and as a supertranslation on C_barz barz, and this resolves the phase-space problem of He et al. without imposing boundary conditions at spacelike infinity. That is a solid result, and the careful treatment of total derivatives when metric coefficients are not regular on the sphere is a genuine contribution. The appendix constructions of Kerr and Taub-NUT in Bondi coordinates are also useful and carefully done.

The advertised soft NUT theorem, though, is not actually derived. The paper stops at a Ward identity and then asserts the theorem. The quantum conservation equation (4.2) is labeled conjectural, and the action of the charge on scattering states in (4.17)–(4.18) is posited rather than derived. That is honest, but it means the central claim is conditional on assumptions outside the classical computation. The paper deserves credit for flagging this, but a reader should not come away thinking a soft NUT theorem has been established.

The factor-of-1/2 problem is the more concrete worry. Section 3 shows that the revised dual charge for Taub-NUT evaluates to −ℓ/(2G), half the Komar dual energy. The authors acknowledge this and say no analogue of the k·B term amends it. That is load-bearing: the complexified charge Q0 used in the brackets and in the scattering-state action is built from this tilde{Q}, so the eigenvalues tilde{E} in (4.17) are not obviously the physical NUT charges. If the normalization is off, the soft factors in the claimed theorem are off too. This is not a minor inconvenience; it undermines the physical interpretation of the soft theorem. The authors' appeal to the Iyer–Wald analogy suggests there may be a missing boundary term, and if that term exists, the brackets and the theorem could change. The paper would be stronger if it either fixed this or explicitly stated that tilde{E} is a different quantity whose relation to NUT charge is not yet understood.

Despite these issues, this is a serious paper. The phase-space result is new and correct, the generalization of asymptotic flatness is well motivated, and the comparison with the electromagnetic magnetic soft theorem is apt. It deserves a proper peer review, not a desk rejection. I would recommend acceptance after revision, with the soft NUT theorem reframed as a conjecture and the normalization issue either resolved or clearly separated from the charge used in the Ward identity. As it stands, the abstract overclaims what the paper actually shows.

Referee Report

4 major / 4 minor

Summary. The paper studies dual supertranslation charges in Bondi-Sachs asymptotically flat spacetimes, relaxing the regularity of tensor fields on the 2-sphere so that Taub-NUT-type configurations are admitted. It rederives the standard and dual supertranslation charges including total-derivative terms (Section 3), constructs the complexified charge Q0 = Q - i\tilde Q, and computes its Dirac brackets with radiative modes, obtaining that Q+ generates a time translation on Czz and a supertranslation on C\bar z \bar z (equations (3.21)-(3.22)). It then argues that conservation of this complexified charge across null infinity leads to a Ward identity and a new soft NUT/graviton theorem (Section 4).

Significance. If correct, the paper would connect dual/NUT charges to the soft-graviton/BMS framework and would remove the need for a boundary condition at spacelike infinity that otherwise excludes NUT charges. The phase-space bracket computation (3.21)-(3.22) is clean and explicit, and the Bondi-coordinate expansions for Kerr and Taub-NUT in Appendices A and B are useful checkable data. However, the advertised soft NUT theorem is not actually derived in the manuscript: it rests on a quantum Ward identity that the paper itself calls conjectural, and it is not stated as an explicit S-matrix soft formula. The unresolved factor of 1/2 between the revised dual charge and the Komar dual energy also leaves the physical interpretation of the charge entering the would-be theorem ambiguous.

major comments (4)

[Section 4, equations (4.2) and (4.16)-(4.19)] The revised dual charge for Taub-NUT is \tilde Q_0^{(int)}(s=1) = -ℓ/(2G), exactly half the Komar dual energy \tilde M_K = ℓ/G, and the paper states that the factor is not amended. This is load-bearing because \tilde Q enters the complexified charge Q0 in (3.9), the Dirac brackets (3.21)-(3.22), and the scattering-state eigenvalues \tilde E in (4.17). If \tilde Q is the correct conserved charge, then the would-be soft theorem is naturally expressed in units of \tilde Q, not the usual NUT parameter ℓ, and the identification of \tilde E with the physical NUT charge is not established; if the Komar value ℓ/G is the physical NUT charge, then the charge derivation omits a boundary term analogous to k·B in (3.6), and the brackets (3.21)-(3.22) would not describe the physical NUT charge. The manuscript needs to explicitly settle which quantity defines the NUT charge appearing in the proposed theorem.
[Section 4, after equation (4.19)] The derivation of the soft NUT theorem assumes the quantum Ward identity Q+ S - S Q- = 0, which the paper explicitly labels as conjectural in the paragraph after (4.2). The subsequent steps, including the state actions (4.17)-(4.18) and the final identity (4.19), are algebraic consequences of this assumption. The paper's central claim is therefore conditional on an unproved input. The authors should either prove this conservation law in a well-defined sector of the quantum theory, or reformulate the conclusion as a conditional statement, clearly separating the classical phase-space result from the conjectural soft theorem.
[Section 3, equation (3.14)] The paper never states the claimed 'soft NUT/graviton theorem' as an explicit S-matrix formula. Choosing s(w) = 1/(z-w) yields only a Ward identity; no soft limit, no soft factor, and no comparison with known Weinberg soft factors are displayed. Without this, the abstract's claim that the charges 'imply a new soft NUT theorem' overstates what has been shown. The theorem should be stated explicitly and derived, or the claims should be reduced to a proposed Ward identity awaiting further confirmation.
[Section 3, equation (3.14)] The phase-space argument assumes Q0|_{I^+_+} = 0 in (3.14), and Section 4 similarly assumes vanishing of the charge at I^-_-. Although the paper calls (3.14) technical, it is a boundary condition at future null infinity, and its compatibility with non-trivial NUT sectors is not demonstrated. The claim that the inclusion of dual charges removes the need for boundary conditions should therefore be qualified: the construction still imposes conditions at the ends of null infinity, even if not at spacelike infinity.

minor comments (4)

[Page 8, after equation (2.20)] The phrase 'It fact, in deriving equation (2.15)...' appears to contain a typo and should read 'In fact, in deriving equation (2.15)...'.
[Equations (2.15)-(2.20) and (3.2)-(3.5)] The notation alternates between \tilde Q_0, \tilde Q_0^{(int)}, and \tilde Q^{(int)}_0 without consistent subscripts; harmonizing the notation would improve readability.
[Section 2.1, footnote 7] The sign convention between the dual charge and the Komar dual energy is described only in a footnote; an explicit sign summary or a table of conventions would help the reader track the factor of 1/2 discussion.
[Appendix B] The displayed Bondi-coordinate expansions are dense and mix half-angle and secant/tangent forms; giving simplified expressions for the leading singular terms such as C_{\theta\phi} and C_{0\phi} would make the singularity structure and the comparison with Ref. [6] easier to verify.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the classical charge/bracket derivation is self-contained, and the soft NUT theorem is explicitly conditional on a conjectural Ward identity.

full rationale

The paper's classical derivation is self-contained: equations (3.1)-(3.2) define the revised supertranslation and dual charges, and (3.19)-(3.22) compute their Dirac brackets directly from the radiative bracket (3.19). No parameter is fitted and then relabelled as a prediction. The soft NUT theorem in section 4 is not presented as a consequence of the phase-space calculation alone. The paper begins with the conservation law Q+ = Q- (4.4), explicitly states that the quantum identity (4.2) 'has so far been conjectural,' and introduces the state action (4.17)-(4.18) as an identification. Equation (4.19) is then a direct transcription of those assumptions with s(w)=1/(z-w), so the theorem is conditional rather than circularly obtained. The acknowledged factor-of-1/2 discrepancy for the Taub-NUT dual charge (3.5), (3.8) and the footnote that the I+_+ boundary condition is technical are limitations, but they do not show that any claimed prediction reduces to its own input by construction. Self-citations to [2,3] supply initial expressions, but the paper rederives the charges, so they are not load-bearing.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The derivation imports standard Bondi fall-offs and Einstein equation results, adopts the null-infinity Dirac bracket from prior work, and assumes a conjectural quantum Ward identity plus a specific action of the complexified charge on scattering states. No data are fitted and no new entities are introduced.

assumptions (6)

domain assumption Bondi metric fall-offs (2.2) and determinant gauge (2.3)
Standard definition of asymptotically flat spacetimes used throughout, extended in section 3 to allow non-regular tensors.
domain assumption Einstein-equation consequences (2.17), (2.18) relating metric components to energy-momentum fall-offs (2.16)
Used to rewrite the dual charge as (2.19) and to derive the flux (3.17).
domain assumption Dirac bracket (3.19) for radiative modes at null infinity
Adopted from Refs. [43,44]; the paper uses it unmodified despite the generalized non-regular fall-offs.
ad hoc to paper Vanishing of the total charge at I^+_+, equation (3.14)
A boundary condition at u = +infinity imposed to derive Q_+; footnote 11 says this may be removable.
ad hoc to paper Quantum Ward identity Q_+S - SQ_- = 0 (4.2)
The load-bearing assumption for the soft NUT theorem; the paper states it 'should ultimately come from the theory' and is conjectural.
ad hoc to paper Action of the charge on scattering states (4.17)-(4.18)
Posits that Q^- acts as sum over particles of (E - i tilde E)s; needed to turn the Ward identity into the soft theorem.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Dual gravitational charges and soft theorems." pith.science (2026). https://pith.science/paper/ELFBDMAJ

@misc{pith2026190801164,
  author       = {Pith},
  title        = {Pith review of: Dual gravitational charges and soft theorems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ELFBDMAJ}},
  note         = {Machine review of arXiv:1908.01164}
}

read the original abstract

We consider the consequences of the dual gravitational charges for the phase space of radiating modes, and find that they imply a new soft NUT theorem. In particular, we argue that the existence of these new charges removes the need for imposing boundary conditions at spacelike infinity that would otherwise preclude the existence of NUT charges.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Memory effect from the scattering of Taub-NUT black holes
hep-th 2026-03 conditional novelty 7.0 of 10

Soft theorems yield a gauge-invariant nutty soft factor and the associated memory tensor for Kerr-Taub-NUT scattering, with magnetic components and directional divergences absent in electromagnetism.
Asymptotic Structure of Einstein-Maxwell-Dilaton Theory and Its Five Dimensional Origin
hep-th 2019-09 accept novelty 6.0 of 10

The asymptotic solution space and mass-loss formula for Einstein-Maxwell-dilaton theory are derived, and the Kaluza-Klein case is shown to match five-dimensional pure Einstein gravity.
Quasi-local conserved charges in General Relativity
gr-qc 2019-08 conditional novelty 6.0 of 10

The paper constructs a general prescription for quasi-local conserved charges in GR and proposes the zero-mode BMS charge in Newman-Unti gauge as a quasi-local energy candidate.
Dressed States Call for Logarithmic Asymptotic Symmetries
hep-th 2026-07 conditional novelty 5.0 of 10

Dressed particles with soft-boson clouds are irreducible unitary representations of asymptotic symmetry groups only after adding logarithmic 'dual' symmetries, which supply the needed Heisenberg central extension.
Taub-NUT from the Dirac monopole
hep-th 2019-08 conditional novelty 5.0 of 10

Choosing the Bondi gauge field C0 to be a Dirac monopole yields the Taub-NUT metric in Bondi coordinates.
GGI lectures on boundary and asymptotic symmetries
hep-th 2025-12 conditional novelty 4.0 of 10

A lecture-note review of boundary and asymptotic symmetries that re-derives the BMS group as the asymptotic symmetry group of Minkowski spacetime alone and constructs an integral Hamiltonian generator for scalar-field...

Reference graph

Works this paper leans on

48 extracted references · 14 canonical work pages · cited by 6 Pith papers

[1]

Subleading BMS charges and fake news near null inﬁnity,

H. Godazgar, M. Godazgar, and C. N. Pope, “Subleading BMS charges and fake news near null inﬁnity,” JHEP 01 (2019) 143, arXiv:1809.09076 [hep-th]

arXiv 2019
[2]

New dual gravit ational charges,

H. Godazgar, M. Godazgar, and C. N. Pope, “New dual gravit ational charges,” Phys. Rev. D99 (2019) no. 2, 024013, arXiv:1812.01641 [hep-th]

arXiv 2019
[3]

Tower of sublea ding dual BMS charges,

H. Godazgar, M. Godazgar, and C. N. Pope, “Tower of sublea ding dual BMS charges,” JHEP 03 (2019) 057, arXiv:1812.06935 [hep-th]

arXiv 2019
[4]

New conservation laws for ze ro rest-mass ﬁelds in asymptotically ﬂat space-time,

E. T. Newman and R. Penrose, “New conservation laws for ze ro rest-mass ﬁelds in asymptotically ﬂat space-time,” Proc. Roy. Soc. Lond. A305 (1968) 175–204

work page 1968
[5]

BMS charge algebra,

G. Barnich and C. Troessaert, “BMS charge algebra,” JHEP 12 (2011) 105, arXiv:1106.0213 [hep-th]

arXiv 2011
[6]

Properties of Dual Supertranslat ion Charges in Asymptotically Flat Spacetimes,

U. Kol and M. Porrati, “Properties of Dual Supertranslat ion Charges in Asymptotically Flat Spacetimes,” arXiv:1907.00990 [hep-th]

arXiv 1907
[7]

Dual-mass in general relativit y,

S. Ramaswamy and A. Sen, “Dual-mass in general relativit y,” J.Math.Phys. 22 (1981) 2612

work page 1981
[8]

NUT 4-momenta are forever,

A. Ashtekar and A. Sen, “NUT 4-momenta are forever,” Journal of Mathematical Physics 23 (1982) no. 11, 2168–2178. 21

work page 1982

Show all 48 references

[9]

Empty space-times admitting a three paramet er group of motions,

A. H. Taub, “Empty space-times admitting a three paramet er group of motions,” Annals of Mathematics 53 (1951) no. 3, 472–490

1951
[10]

Empty space gener alization of the schwarzschild metric,

E. Newman, L. Tamburino, and T. Unti, “Empty space gener alization of the schwarzschild metric,” Journal of Mathematical Physics 4 (1963) no. 7, 915–923

1963
[11]

BMS supert ranslations and Weinberg’s soft graviton theorem,

T. He, V. Lysov, P. Mitra, and A. Strominger, “BMS supert ranslations and Weinberg’s soft graviton theorem,” JHEP 05 (2015) 151, arXiv:1401.7026 [hep-th]

2015 arXiv
[12]

Infrared photons and gravitons,

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

1965
[13]

Asymptotic Symmetries of Yang-Mills T heory,

A. Strominger, “Asymptotic Symmetries of Yang-Mills T heory,” JHEP 07 (2014) 151, arXiv:1308.0589 [hep-th]

2014 arXiv
[14]

On BMS Invariance of Gravitational Sca ttering,

A. Strominger, “On BMS Invariance of Gravitational Sca ttering,” JHEP 07 (2014) 152, arXiv:1312.2229 [hep-th]

2014 arXiv
[15]

N ew Symmetries of Massless QED,

T. He, P. Mitra, A. P. Porfyriadis, and A. Strominger, “N ew Symmetries of Massless QED,” JHEP 10 (2014) 112, arXiv:1407.3789 [hep-th]

2014 arXiv
[16]

Gravitational Memory , BMS Supertranslations and Soft Theorems,

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

2016 arXiv
[17]

Magnetic Corrections to the Soft Photo n Theorem,

A. Strominger, “Magnetic Corrections to the Soft Photo n Theorem,” Phys. Rev. Lett. 116 (2016) no. 3, 031602, arXiv:1509.00543 [hep-th]

2016 arXiv
[18]

Soft Hair on Black Holes,

S. W. Hawking, M. J. Perry, and A. Strominger, “Soft Hair on Black Holes,” Phys. Rev. Lett. 116 (2016) no. 23, 231301, arXiv:1601.00921 [hep-th]

2016 arXiv
[19]

Residual diﬀeomorphisms and sym plectic soft hairs: The need to reﬁne strict statement of equivalence principle,

M. M. Sheikh-Jabbari, “Residual diﬀeomorphisms and sym plectic soft hairs: The need to reﬁne strict statement of equivalence principle,” Int. J. Mod. Phys. D25 (2016) no. 12, 1644019, arXiv:1603.07862 [hep-th]

2016 arXiv
[20]

Superrot ation Charge and Supertranslation Hair on Black Holes,

S. W. Hawking, M. J. Perry, and A. Strominger, “Superrot ation Charge and Supertranslation Hair on Black Holes,” JHEP 05 (2017) 161, arXiv:1611.09175 [hep-th]

2017 arXiv
[21]

BMS Supertranslations and Not So So ft Gravitons,

E. Conde and P. Mao, “BMS Supertranslations and Not So So ft Gravitons,” JHEP 05 (2017) 060, arXiv:1612.08294 [hep-th] . 22

2017 arXiv
[22]

Asymptotic Dynamics in Perturbative Quantum Gravity and BMS Supertranslations,

S. Choi, U. Kol, and R. Akhoury, “Asymptotic Dynamics in Perturbative Quantum Gravity and BMS Supertranslations,” JHEP 01 (2018) 142, arXiv:1708.05717 [hep-th]

2018 arXiv
[23]

Asympt otic symmetries and charges at null inﬁnity: from low to high spins,

A. Campoleoni, D. Francia, and C. Heissenberg, “Asympt otic symmetries and charges at null inﬁnity: from low to high spins,” EPJ Web Conf. 191 (2018) 06011, arXiv:1808.01542 [hep-th]

2018 arXiv
[24]

Asymptotic charges in mass less QED revisited: A view from Spatial Inﬁnity,

M. Campiglia and A. Laddha, “Asymptotic charges in mass less QED revisited: A view from Spatial Inﬁnity,” arXiv:1810.04619 [hep-th]

arXiv
[25]

More on gravitational memory,

P. Mao and X. Wu, “More on gravitational memory,” JHEP 05 (2019) 058, arXiv:1812.07168 [gr-qc]

2019 arXiv
[26]

A Note on th e Subleading Soft Graviton,

E. Himwich, Z. Mirzaiyan, and S. Pasterski, “A Note on th e Subleading Soft Graviton,” arXiv:1902.01840 [hep-th]

1902 arXiv
[27]

Holographi c Renormalization in Flat Space: Symplectic Potential and Charges of Electromagnetism,

L. Freidel, F. Hopfm¨ uller, and A. Riello, “Holographi c Renormalization in Flat Space: Symplectic Potential and Charges of Electromagnetism,” arXiv:1904.04384 [hep-th]

1904 arXiv
[28]

Strollin g along gravitational vacua,

E. S. Kutluk, A. Seraj, and D. Van Den Bleeken, “Strollin g along gravitational vacua,” arXiv:1904.12869 [hep-th]

1904 arXiv
[29]

Celestial amplitude s and conformal soft theorems,

T. Adamo, L. Mason, and A. Sharma, “Celestial amplitude s and conformal soft theorems,” arXiv:1905.09224 [hep-th]

1905 arXiv
[30]

A note on the symplectic struc ture of asymptotically ﬂat gravity and BMS symmetries,

F. Alessio and M. Arzano, “A note on the symplectic struc ture of asymptotically ﬂat gravity and BMS symmetries,” arXiv:1906.05036 [gr-qc]

1906 arXiv
[31]

A Classical Proof of the Classical Soft Graviton Theorem in D>4,

A. Laddha and A. Sen, “A Classical Proof of the Classical Soft Graviton Theorem in D>4,” arXiv:1906.08288 [gr-qc]

1906 arXiv
[32]

New Magnetic Symmetries in ( d + 2)-Dimensional QED,

T. He and P. Mitra, “New Magnetic Symmetries in ( d + 2)-Dimensional QED,” arXiv:1907.02808 [hep-th]

1907 arXiv
[33]

Subleading soft dressings of as ymptotic states in QED and perturbative quantum gravity,

S. Choi and R. Akhoury, “Subleading soft dressings of as ymptotic states in QED and perturbative quantum gravity,” arXiv:1907.05438 [hep-th]

1907 arXiv
[34]

Symmetries of asymptoti cally ﬂat 4 dimensional spacetimes at null inﬁnity revisited,

G. Barnich and C. Troessaert, “Symmetries of asymptoti cally ﬂat 4 dimensional spacetimes at null inﬁnity revisited,” Phys. Rev. Lett. 105 (2010) 111103, arXiv:0909.2617 [gr-qc] . 23

2010 arXiv
[35]

Aspects of the BMS/CFT co rrespondence,

G. Barnich and C. Troessaert, “Aspects of the BMS/CFT co rrespondence,” JHEP 05 (2010) 062, arXiv:1001.1541 [hep-th]

2010 arXiv
[36]

Grav itational waves in general relativity: 7. Waves from axisymmetric isolated sy stems,

H. Bondi, M. G. J. van der Burg, and A. W. K. Metzner, “Grav itational waves in general relativity: 7. Waves from axisymmetric isolated sy stems,” Proc. Roy. Soc. Lond. A269 (1962) 21–52

1962
[37]

Gravitational waves in general relativit y: 8. Waves in asymptotically ﬂat space-times,

R. K. Sachs, “Gravitational waves in general relativit y: 8. Waves in asymptotically ﬂat space-times,” Proc. Roy. Soc. Lond. A270 (1962) 103–126

1962
[38]

Stephani, D

H. Stephani, D. Kramer, M. A. H. MacCallum, C. Hoenselae rs, and E. Herlt, Exact solutions of Einstein ’s ﬁeld equations . Cambridge Monographs on Mathematical Physics. Cambridge Univ. Press, Cambridge, 2 003
[39]

Hamiltonian structure and asymptotic symmetries of the Einstein-Maxwell system at spatial inﬁnity,

M. Henneaux and C. Troessaert, “Hamiltonian structure and asymptotic symmetries of the Einstein-Maxwell system at spatial inﬁnity,” JHEP 07 (2018) 171, arXiv:1805.11288 [gr-qc]

2018 arXiv
[40]

The asymptotic structu re of gravity at spatial inﬁnity in four spacetime dimensions,

M. Henneaux and C. Troessaert, “The asymptotic structu re of gravity at spatial inﬁnity in four spacetime dimensions,” arXiv:1904.04495 [hep-th]

1904 arXiv
[41]

Asymptotic Flatness, Taub-NUT, and Varia tional Principle,

A. Virmani, “Asymptotic Flatness, Taub-NUT, and Varia tional Principle,” Phys. Rev. D84 (2011) 064034, arXiv:1106.4372 [hep-th]

2011 arXiv
[42]

Some properties of Noether charg e and a proposal for dynamical black hole entropy,

V. Iyer and R. M. Wald, “Some properties of Noether charg e and a proposal for dynamical black hole entropy,” Phys. Rev. D50 (1994) 846–864, arXiv:gr-qc/9403028 [gr-qc]

1994 arXiv
[43]

Symplectic Geometry of Ra diative Modes and Conserved Quantities at Null Inﬁnity,

A. Ashtekar and M. Streubel, “Symplectic Geometry of Ra diative Modes and Conserved Quantities at Null Inﬁnity,” Proc. Roy. Soc. Lond. A376 (1981) 585–607

1981
[44]

Ashtekar, Asymptotic quantization: Based on 1984 Naples lectures

A. Ashtekar, Asymptotic quantization: Based on 1984 Naples lectures . Bibliopolis, 1987

1984
[45]

Asymptotic symmetries of electromagnetism at spatial inﬁnity,

M. Henneaux and C. Troessaert, “Asymptotic symmetries of electromagnetism at spatial inﬁnity,” JHEP 05 (2018) 137, arXiv:1803.10194 [hep-th]

2018 arXiv
[46]

Lectures on the Infrared Structure of G ravity and Gauge Theory,

A. Strominger, “Lectures on the Infrared Structure of G ravity and Gauge Theory,” arXiv:1703.05448 [hep-th] . 24

arXiv
[47]

Gravitationa l multi-NUT solitons, Komar masses and charges,

G. Bossard, H. Nicolai, and K. S. Stelle, “Gravitationa l multi-NUT solitons, Komar masses and charges,” Gen. Rel. Grav. 41 (2009) 1367–1379, arXiv:0809.5218 [hep-th]

2009 arXiv
[48]

The Kerr spacetime in generalized Bondi–Sachs coordinate s,

S. J. Fletcher and A. W. C. Lun, “The Kerr spacetime in generalized Bondi–Sachs coordinate s,”Class. Quant. Grav. 20 (sep, 2003) 4153–4167. 25

2003

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Subleading BMS charges and fake news near null inﬁnity,

H. Godazgar, M. Godazgar, and C. N. Pope, “Subleading BMS charges and fake news near null inﬁnity,” JHEP 01 (2019) 143, arXiv:1809.09076 [hep-th]

arXiv 2019

[2] [2]

New dual gravit ational charges,

H. Godazgar, M. Godazgar, and C. N. Pope, “New dual gravit ational charges,” Phys. Rev. D99 (2019) no. 2, 024013, arXiv:1812.01641 [hep-th]

arXiv 2019

[3] [3]

Tower of sublea ding dual BMS charges,

H. Godazgar, M. Godazgar, and C. N. Pope, “Tower of sublea ding dual BMS charges,” JHEP 03 (2019) 057, arXiv:1812.06935 [hep-th]

arXiv 2019

[4] [4]

New conservation laws for ze ro rest-mass ﬁelds in asymptotically ﬂat space-time,

E. T. Newman and R. Penrose, “New conservation laws for ze ro rest-mass ﬁelds in asymptotically ﬂat space-time,” Proc. Roy. Soc. Lond. A305 (1968) 175–204

work page 1968

[5] [5]

BMS charge algebra,

G. Barnich and C. Troessaert, “BMS charge algebra,” JHEP 12 (2011) 105, arXiv:1106.0213 [hep-th]

arXiv 2011

[6] [6]

Properties of Dual Supertranslat ion Charges in Asymptotically Flat Spacetimes,

U. Kol and M. Porrati, “Properties of Dual Supertranslat ion Charges in Asymptotically Flat Spacetimes,” arXiv:1907.00990 [hep-th]

arXiv 1907

[7] [7]

Dual-mass in general relativit y,

S. Ramaswamy and A. Sen, “Dual-mass in general relativit y,” J.Math.Phys. 22 (1981) 2612

work page 1981

[8] [8]

NUT 4-momenta are forever,

A. Ashtekar and A. Sen, “NUT 4-momenta are forever,” Journal of Mathematical Physics 23 (1982) no. 11, 2168–2178. 21

work page 1982