GGI lectures on boundary and asymptotic symmetries

Simone Speziale

REVIEW 2 major objections 5 minor 1 cited by

GGI lectures on boundary and asymptotic symmetries

T0 review · 2 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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

Pith's one-line read These lecture notes derive the BMS group—supertranslations together with Lorentz transformations—as the asymptotic symmetry group of Minkowski spacetime, using only the requirement that the leading conformally compactified metric be preserv

desk verdict Honest, accurate lecture notes; the BMS 'derivation' is conditional on a fall-off assumption and the v2 text needs cleanup, but the pedagogical content is solid and worth referee time. read the letter →

arxiv 2512.16810 v3 pith:ICRA3R7F submitted 2025-12-18 hep-th gr-qc

Simone Speziale This is my paper · ORCID

classification hep-thgr-qc MSC 83C3083C40

keywords BMSgroupasymptoticsymmetriesnullinfinityconformalcompactificationsupertranslationscovariantphasespaceNoetherchargeshypersurfaces

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

The paper tries to establish that the BMS asymptotic symmetry group is fixed by flat-space asymptotics alone: asking vector fields to preserve only the leading order of the conformally compactified Minkowski metric at future null infinity yields precisely the algebra of supertranslations and sphere conformal Killing vectors, exponentiating to SL(2,C) ⋉ R^S. This gives a derivation of BMS that does not require solving Einstein equations or assuming the full asymptotic expansion. The same lecture notes review how Noether charges and flux-balance laws follow from the covariant phase space, and include an original construction of an integral Hamiltonian generator for diffeomorphisms of a scalar field on a null hypersurface. If correct, this fixes BMS as the natural asymptotic symmetry group within the chosen fall-off class and supplies a minimal toy model for null-boundary charges.

What carries the argument

The load-bearing tool is conformal compactification: rescaling Minkowski by Ω² = 1/r² makes future null infinity a smooth null boundary with unphysical metric η̂_μν. The key equation is the leading-order preservation condition £_ξ η̂_μν|_{I} = 2α_ξ η̂_μν, which replaces the Killing equation and fixes the asymptotic Killing vectors. The BMS group—the semi-direct product of sphere conformal Killing vectors (Lorentz transformations) with supertranslations, arbitrary angle-dependent time translations—is the object derived. For the charge sector, the covariant phase space and the covariance/stationarity prescription for resolving the ambiguities of the symplectic potential are what turn Noether c

What would settle it

Compute the full solution space of £_ξ η̂_μν|_{I} = 2α_ξ η̂_μν for the conformally compactified Minkowski metric under the paper's regularity assumptions; if any solution exists that is not of the form in Eq. (5.16), or if the Lie bracket of two solutions fails to close into the stated algebra, the central claim is false.

Watch

Extended reading notes

Core claim

The central claim is that the BMS group is already fully determined by Minkowski spacetime. With the conformally compactified metric η̂_μν and the requirement £_ξ η̂_μν|_{I} = 2α_ξ η̂_μν, the allowed vector fields take the form ξ = f ∂_u + Y^A ∂_A + Ω(ḟ ∂_Ω − D_A f ∂^A) + O(Ω²), where f = T(x^A) + (u/2) D_A Y^A and T is an arbitrary function on the sphere. These vector fields close under the Lie bracket and exponentiate to the BMS group, G_BMS = SL(2,C) ⋉ R^S, with SL(2,C) acting as conformal Killing vectors of the sphere and R^S as supertranslations. The notes also show that the same group results from preserving standard null-infinity fall-off conditions, and that the associated charges a

Load-bearing premise

The derivation stands or falls with the modeling choice that asymptotic symmetries need preserve only the leading order of the unphysical metric at null infinity; change the fall-off condition and the resulting symmetry group changes.

Editorial extensions

If this is right

The BMS group follows from the leading-order conformal structure of Minkowski alone; the standard null-infinity fall-off analysis reproduces the same vector fields, so the two derivations agree.
Supertranslations are arbitrary functions on the sphere; only their l=0,1 modes are global translations, and there is no unique Lorentz subgroup—it depends on a choice of supertranslation frame.
BMS charges are surface integrals with flux-balance laws; fixing symplectic-potential ambiguities by covariance and stationarity makes the charges background-independent and removes field-dependent cocycles from the charge algebra.
The same covariant-phase-space methods applied to finite null boundaries yield a hierarchy of boundary symmetry groups, from all diffeomorphisms of the null hypersurface to BMS-like groups with an extra dilation.
The scalar field on a null hypersurface admits an explicit integral Hamiltonian generator, providing a tractable model for boundary charges and fluxes outside gravity.

Reading between the lines

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

Editorial inference: the derivation is sensitive to the fall-off class: if the requirement in Eq. (5.15) is weakened to allow subleading terms in the unphysical metric, larger asymptotic symmetry groups (generalized or extended BMS) arise, so the paper's Minkowski-only derivation fixes BMS within a specific fall-off class rather than ruling out larger groups.
Editorial inference: the same leading-order conformal logic could be applied to other spacetimes with conformal boundaries, such as de Sitter or anti-de Sitter, to identify their asymptotic symmetry groups without solving the full field equations.
Editorial inference: the scalar null-hypersurface Hamiltonian generator suggests a concrete check—quantize the scalar field on the null boundary and verify that the generator's bracket reproduces the diffeomorphism action; this could be a toy model for edge-mode Hilbert spaces in flat holography.

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

Read the GGI notes by Speziale. Punchline: this is a useful, mostly reliable pedagogical review of boundary and asymptotic symmetries, with two appendices that advertise original results. The visible math checks out — the Komar charge, Iyer–Wald relation, BMS vector fields and algebra, and the flux-balance laws all match the standard literature at each point I could cross-check. The writing is clear, and the paper is openly self-limiting: it declares the personal viewpoint and concedes the symplectic potential is not unique. That is real credit.

The advertised novelty is smaller than the abstract suggests. The BMS derivation in §5.2 is conditional on eq. (5.15), which imposes a particular fall-off on the unphysical metric. The paper itself notes that weaker fall-offs give larger symmetry groups. So 'using only Minkowski' overstates the input; the derivation fixes BMS within a chosen class, not from flatness alone. That does not make the derivation wrong, but it puts the novelty claim in proportion. The genuinely new item, Appendix B, I could not verify from the text available to me; it would need a careful check before anyone leans on it.

The v2 draft is not yet stable school material: §5.2–5.3 contain duplicated passages and unresolved [?] citations that should have been cleaned before posting. That is minor in scope but real.

Net: this is a honest consolidation of known results and a reasonable entry point for newcomers. It is not a breakthrough. I would send it to peer review — the pedagogical value and the unverified appendix justify referee time — but I would expect the referee to ask for cleanup and to soften the 'using only Minkowski' phrasing. I would not cite it in my own work in the next year; it is support material rather than a research result I need.

Referee Report

2 major / 5 minor

Summary. The manuscript is an expanded set of lecture notes for a GGI school on asymptotic symmetries and flat holography. It reviews the covariant phase space, Noether's theorem for gauge theories and gravity, boundary and asymptotic symmetries, flux-balance laws on null boundaries, and BMS charges and fluxes at null infinity. The two claimed original contributions are: (i) a derivation of the BMS group from Minkowski spacetime in Penrose conformal compactification, presented in §5.2 and Appendix A; and (ii) a derivation of an integral Hamiltonian generator for a scalar field on a null hypersurface, in Appendix B. The BMS derivation is summarized by Eq. (5.15)–(5.23), where the condition that the unphysical metric be preserved to leading order at I leads to the algebra (5.22) and the group G_BMS = SL(2,C) ⋉ R^S.

Significance. As a set of lecture notes, the paper is useful and mostly reliable: the covariant-phase-space review is systematic, the formulas agree at cross-checkable points with the established literature (Komar charge (3.54), Iyer–Wald relation (3.58), Bondi flux-balance laws (5.35)–(5.36), BMS algebra (5.22) and vector fields (5.41)), and the discussion of polarizations and Wald–Zoupas covariance is pedagogically valuable. The BMS derivation, if properly qualified, is a nice self-contained route from (5.15) to (5.23). However, the headline novelty is not assumption-free: the group follows from the fall-off prescription (5.15), and the abstract's claim that BMS is derived 'using only Minkowski' overstates the input. The scalar null-boundary toy model in Appendix B is potentially interesting but is not developed in the main text.

major comments (2)

[§5.2 / Abstract / §5.3] The abstract's claim of an 'original derivation of the BMS group using only Minkowski' is not accurate as stated. The derivation rests on Eq. (5.15), £_ξ η̂_μν |_I = 2α_ξ η̂_μν, which is a fall-off / boundary condition on asymptotic vector fields, not a consequence of flatness alone. The exact Killing condition (5.14) gives Poincaré, while weaker fall-offs—explicitly acknowledged in §5.3 ('the analysis can be extended to weaker fall-off conditions and larger symmetries than BMS')—give larger groups such as gBMS/extended BMS. Thus the derived group is conditional on the fall-off class (5.15) (equivalently the Bondi-type conditions (5.40)). The abstract and §5.2 should be reworded to state clearly 'under the standard leading-order conformal-preservation fall-offs (5.15)', and the dependence of the group on this modeling choice should be emphasized. This is load-bearing because it is the pa
[§5.2, Eq. (5.16)] The statement that the vector fields (5.16) 'form a closed sub-algebra' needs an explicit equivalence-relation or quotient. Equation (5.16) leaves all O(Ω^2) terms undetermined, so the algebra statement is only true up to vector fields that vanish at I (or some analogous trivial-diffeomorphism quotient). Without specifying this quotient, the set of vector fields (5.16) is not a well-defined group of equivalence classes. The Bondi-Sachs extension (5.41) in §5.3 fixes the higher-order terms, but §5.2 presents the Minkowski derivation as self-contained. Please state the quotient explicitly or refer more precisely to the treatment in Appendix A.

minor comments (5)

[§5.2, around Eq. (5.16)] There is an apparent typesetting/insertion error: after Eq. (5.16) the text breaks into an unnumbered list ('1. in the early stationary epoch...') followed by duplicated Bondi-Sachs paragraphs and equations labelled (2.38)–(2.48) that do not belong in this section. These should be removed.
[§5.2, before Eq. (5.23)] The phrase 'this algebra exponentiates to a finite group action' is misleading: the group G_BMS = SL(2,C) ⋉ R^S is not finite. This should read 'finite-dimensional group action' or 'action of a finite-dimensional group'.
[§5.2, Eq. (5.23)] The notation R^S is used without definition; while the text later explains that T(x^A) is an arbitrary function on the sphere, the definition should be given at first use.
[§2.2–§2.3] The paper repeatedly identifies closed forms with exact forms by assuming trivial cohomology. In §2.2 this is justified by a theorem for local forms in the variational bicomplex, but in §2.3 the wording 'assuming that the field space has trivial topology' is used. Please clarify the distinction between spacetime and field-space cohomology, since this assumption underlies the charge-aspect uniqueness claims.
[Abstract / Appendix B] The second claimed original contribution, the Hamiltonian generator for a scalar field on a null hypersurface, is announced in the abstract but not summarized or connected to the main text (e.g., Section 4.2). If it is a novel contribution, a short outline or cross-reference should be added in the introduction or conclusions.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the BMS derivation is a self-contained PDE calculation from an explicit fall-off condition; self-citations are contextual, not load-bearing.

full rationale

Walking the claimed derivation chain, the asserted novelty — the BMS group from Minkowski asymptotics (§5.2, Eqs. 5.15→5.16→5.23) — is a self-contained calculation. The input is the explicit fall-off/preservation condition (5.15) on the conformally compactified metric, and the output (5.16) is the solution space of that condition, not a restatement of it. The paper is transparent that (5.15) is a modeling assumption, and §5.3 explicitly says weaker fall-offs give larger symmetries; this is an acknowledged limitation, not a hidden identification of conclusion with hypothesis. The same BMS group is independently obtained in §5.3 from Bondi–Sachs residual diffeomorphisms, providing a second, external route to the result. The generalized Wald–Zoupas framework in §2.6 and §4 draws on the author's own [34] and [54], but those are contextual framework choices anchored to the original Wald–Zoupas paper [6] and do not enter the derivation of (5.23); no fitted parameter is relabeled as a prediction. No equation in the visible text reduces by construction to its input, and the Appendix B scalar generator is not present in the excerpt, so there is no evidence of circularity there.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The paper introduces no fitted constants. Its load-bearing inputs are standard mathematical assumptions (trivial cohomology, field-space exactness) — explicitly flagged by the author — and domain assumptions (asymptotic-flatness class and the existence of a stationary no-flux subclass). What the reader pays for 'upstream' is the stationarity criterion: the uniqueness of charges is asserted as a physical principle (§3.5), with the author conceding uniqueness is not guaranteed. The (b,c) parameters are hand-chosen per context. No new particles, forces, or invented entities are postulated.

free parameters (2)

(b, c) polarization parameters on a null boundary = b ∈ {0, 2, 2/3}; c ∈ {0, 1, 2} in the examples (Tables 4–6)
Hand-selected in §4.1–4.2 to implement different boundary conditions; the general null-boundary charges (4.32) explicitly depend on (b, c), so 'the' surface charge of the formalism is defined only up to this modeling choice. These are not fitted to data — but they are chosen by hand to make the desired flux/vanish properties work.
notion of stationarity (p = 0 locus)
§2.6/Table 3: varies by context (non-expanding horizons vs flat null cones), and the ORBS choice (c=1) was introduced precisely to include flat null cones as stationary; charges/fluxes change with this choice, so it is a hand-chosen input to the 'generalized Wald–Zoupas' selection.

assumptions (4)

standard math Trivial cohomology in field space and on spacetime, so closed forms are exact (and closed 0-forms are constants).
Stated explicitly in §2.2 ('a p-form functional... closed everywhere in field space is also necessarily exact... [15]') and §2.3 ('assuming trivial cohomology, so that every positive-degree closed form is also exact'); it underlies the central equivalence class (2.36), the split into integrable/non-integrable terms, and the treatment of central extensions c as constants.
domain assumption Asymptotic flatness: conformal compactification with unphysical metric smooth at Ω=0, Bondi gauge conditions (5.25)-(5.33), and the fall-off class (5.38)-(5.40).
§5.1–5.3; the BMS group, the charge aspects (5.52), and the flux-balance laws (5.50) are derived inside this class; the paper notes in §5.3 that weaker fall-offs give larger symmetry groups.
domain assumption A physically-distinguished 'stationary' subclass exists on which the flux vanishes (p = 0), and this selects the preferred symplectic potential.
Table 3 and §2.6 (dissipative case: 'we seek a polarization... such that p vanishes on them'), criteria 1–2 of §3.5; the entire generalized Wald–Zoupas prescription — and hence which charges are 'the' charges — leans on this modeling choice, whose uniqueness the paper concedes is not guaranteed ('If... it is not unique, further analysis would be needed', §2.6).
domain assumption For the tetrad/Holst remark, the connection field equations force Levi-Civita (no torsion) so first- and second-order formulations coincide on-shell.
§2.7, Holst term example: 'In vacuum or with matter Lagrangians not involving the connection, the only solution of the connection equations is Levi-Civita' — used to claim equivalence of the symplectic-potential difference (2.52)-(2.53) with the metric theory.

how reviews work

0 comments

Cite this review

Pith. "Pith review of GGI lectures on boundary and asymptotic symmetries." pith.science (2026). https://pith.science/paper/ICRA3R7F

@misc{pith2026251216810,
  author       = {Pith},
  title        = {Pith review of: GGI lectures on boundary and asymptotic symmetries},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ICRA3R7F}},
  note         = {Machine review of arXiv:2512.16810}
}

read the original abstract

Support material for lectures at the May '25 Galileo Galilei Institute school on asymptotic symmetries and flat holography. Contains an introduction to Noether theorem for gauge theories and gravity, covariant phase space formalism, boundary and asymptotic symmetries, flux-balance laws on null hypersurfaces, future null infinity in Bondi-Sachs coordinates and with Penrose's conformal compactification, BMS symmetries and their charges and fluxes. Includes an original and pedagogical derivation of the BMS group using only Minkowski, and an original derivation of an integral Hamiltonian generator for diffeomorphisms of a scalar field on a null hypersurface.

Figures

Figures reproduced from arXiv: 2512.16810 by the authors.

**Figure 1.** Two space-like hypersurfaces Σ1 and Σ2 joined by a time-like boundary (left panel, T ) or a null boundary (right panel, N ). A useful setup to have in mind when thinking about boundary conditions is a finite region of spacetime, bounded by two space-like hypersurfaces, as in [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

**Figure 2.** Different applications of the co-dimension 2 flux-balance laws. Left panel: On a single spacelike hypersurface Σ with two boundaries, the surface charge difference is determined by the matter content in between. Right panel: Between different times, with dissipative boundary conditions – allowing residual gauge transformations at the boundary, to which ε must belong – the surface charge difference is determined by … view at source ↗

**Figure 3.** Left panel: Different cuts of I , from bottom up: an initial good cut, a translated one and supertranslated one. The translated one is still a good cut, its ray back-tracing identifies a point translated from the origin. The super-translated one is now a bad cut, its ray back-tracing forms caustics and does not identify an point in the bulk of flat spacetime. Right panel: The physical meaning of super-translations:… view at source ↗

Figures from the paper (1 more)

**Figure 3.** Figure 3: Two space-like hypersurfaces ⌃ and ⌃0 intersecting I and delimiting a portion N of it. By the conservation law d! ˆ= 0, the canonical generator on the phase space defined on the portion of I is equal to the di↵erence of the two canonical generators on the space-like hy…

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

Gravitational Memory Beyond Null Infinity through Finite-Distance Carrollian Screens
hep-th 2026-07 conditional novelty 6.0 of 10

Finite-distance null screens carry a Carrollian memory whose leading tracefree large-radius part reproduces the standard Bondi displacement memory in Robinson–Trautman spacetimes.

Reference graph

Works this paper leans on

212 extracted references · 177 linked inside Pith · cited by 1 Pith paper

[1]

Geroch,Asymptotic Structure of Space-Time, ch

R. Geroch,Asymptotic Structure of Space-Time, ch. 1, pp. 1–106. Springer US, Boston, MA, 1977

1977
[2]

Ashtekar,Radiative Degrees of Freedom of the Gravitational Field in Exact General Relativity, J

A. Ashtekar,Radiative Degrees of Freedom of the Gravitational Field in Exact General Relativity, J. Math. Phys.22(1981) 2885–2895

1981
[3]

Ashtekar and M

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

1981
[4]

Dray and M

T. Dray and M. Streubel,Angular momentum at null infinity, Class. Quant. Grav.1(1984), no. 1 15–26

1984
[5]

Dray,Momentum Flux At Null Infinity, Class

T. Dray,Momentum Flux At Null Infinity, Class. Quant. Grav.2(1985) L7–L10

1985
[6]

R. M. Wald and A. Zoupas,A General definition of ’conserved quantities’ in general relativity and other theories of gravity, Phys. Rev. D61(2000) 084027 [gr-qc/9911095]

arXiv 2000
[7]

Ashtekar and S

A. Ashtekar and S. Speziale,Null infinity and horizons: A new approach to fluxes and charges, Phys. Rev. D110(2024), no. 4 044049 [2407.03254]

arXiv 2024
[8]

I. M. Anderson,Introduction to the variational bicomplex, bz Contemporary Mathematics132 (1992)

1992

Show all 212 references

[9]

Barnich, F

G. Barnich, F. Brandt and M. Henneaux,Local BRST cohomology in gauge theories, Phys. Rept.338(2000) 439–569 [hep-th/0002245]

2000 arXiv
[10]

Barnich and F

G. Barnich and F. Brandt,Covariant theory of asymptotic symmetries, conservation laws and central charges, Nucl. Phys.B633(2002) 3–82 [hep-th/0111246]. 18A word of caution about this result: even though the Hamiltonian is well-defined everywhere, the existence of the non-integ...

2002 arXiv
[11]

Forger, C

M. Forger, C. Paufler and H. Roemer,The Poisson bracket for Poisson forms in multisymplectic field theory, Rev. Math. Phys.15(2003) 705–744 [math-ph/0202043]

2003 arXiv
[12]

Khavkine,Covariant phase space, constraints, gauge and the Peierls formula, Int

I. Khavkine,Covariant phase space, constraints, gauge and the Peierls formula, Int. J. Mod. Phys. A29(2014), no. 5 1430009 [1402.1282]

2014 arXiv
[13]

Iyer and R

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

1994 arXiv
[14]

Jacobson, G

T. Jacobson, G. Kang and R. C. Myers,On black hole entropy, Phys. Rev. D49(1994) 6587–6598 [gr-qc/9312023]

1994 arXiv
[15]

R. M. Wald,On identically closed forms locally constructed from a field, J. Math. Phys.31 (1990), no. 10 2378

1990
[16]

Barnich and C

G. Barnich and C. Troessaert,BMS charge algebra, JHEP12(2011) 105 [1106.0213]

2011 arXiv
[17]

A. J. Speranza,Local phase space and edge modes for diffeomorphism-invariant theories, JHEP 02(2018) 021 [1706.05061]

2018 arXiv
[18]

Chandrasekaran and A

V. Chandrasekaran and A. J. Speranza,Anomalies in gravitational charge algebras of null boundaries and black hole entropy, JHEP01(2021) 137 [2009.10739]

2021 arXiv
[19]

Freidel, R

L. Freidel, R. Oliveri, D. Pranzetti and S. Speziale,Extended corner symmetry, charge bracket and Einstein ’s equations, JHEP09(2021) 083 [2104.12881]

2021 arXiv
[20]

Chandrasekaran, E

V. Chandrasekaran, E. E. Flanagan, I. Shehzad and A. J. Speranza,A general framework for gravitational charges and holographic renormalization, Int. J. Mod. Phys. A37(2022), no. 17 2250105 [2111.11974]

2022 arXiv
[21]

Rignon-Bret and S

A. Rignon-Bret and S. Speziale,Covariance and symmetry algebras,2403.00730

arXiv
[22]

G. A. Burnett and R. M. Wald,A conserved current for perturbations of Einstein-Maxwell space-times, Proc. Roy. Soc. Lond. A430(1990), no. 1878 57–67

1990
[23]

De Paoli and S

E. De Paoli and S. Speziale,A gauge-invariant symplectic potential for tetrad general relativity, JHEP07(2018) 040 [1804.09685]

2018 arXiv
[24]

Oliveri and S

R. Oliveri and S. Speziale,Boundary effects in General Relativity with tetrad variables, Gen. Rel. Grav.52(2020), no. 8 83 [1912.01016]

2020 arXiv
[25]

M. P. Reisenberger,The Poisson bracket on free null initial data for gravity, Phys. Rev. Lett. 101(2008) 211101 [0712.2541]

2008 arXiv
[26]

M. P. Reisenberger,The symplectic 2-form for gravity in terms of free null initial data, Class. Quant. Grav.30(2013) 155022 [1211.3880]

2013 arXiv
[27]

M. P. Reisenberger,The Poisson brackets of free null initial data for vacuum general relativity, Class. Quant. Grav.35(2018), no. 18 185012 [1804.10284]

2018 arXiv
[28]

Chandrasekaran and E

V. Chandrasekaran and E. E. Flanagan,Horizon phase spaces in general relativity, JHEP07 (2024) 017 [2309.03871]. 64

2024 arXiv
[29]

Barnich, S

G. Barnich, S. Majumdar, S. Speziale and W.-D. Tan,Lessons from discrete light-cone quantization for physics at null infinity: bosons in two dimensions, JHEP05(2024) 326 [2401.14873]

2024 arXiv
[30]

Harlow and J.-Q

D. Harlow and J.-Q. Wu,Covariant phase space with boundaries, JHEP10(2020) 146 [1906.08616]

2020 arXiv
[31]

Freidel, M

L. Freidel, M. Geiller and D. Pranzetti,Edge modes of gravity. Part I. Corner potentials and charges, JHEP11(2020) 026 [2006.12527]

2020 arXiv
[32]

Margalef-Bentabol and E

J. Margalef-Bentabol and E. J. S. Villase˜ nor,Geometric formulation of the Covariant Phase Space methods with boundaries, Phys. Rev. D103(2021), no. 2 025011 [2008.01842]

2021 arXiv
[33]

Ciambelli, R

L. Ciambelli, R. G. Leigh and P.-C. Pai,Embeddings and Integrable Charges for Extended Corner Symmetry, Phys. Rev. Lett.128(2022) [2111.13181]

2022 arXiv
[34]

G. Odak, A. Rignon-Bret and S. Speziale,Wald-Zoupas prescription with soft anomalies, Phys. Rev. D107(2023), no. 8 084028 [2212.07947]

2023 arXiv
[35]

Compere and D

G. Compere and D. Marolf,Setting the boundary free in AdS/CFT, Class. Quant. Grav.25 (2008) 195014 [0805.1902]

2008 arXiv
[36]

Comp` ere, A

G. Comp` ere, A. Fiorucci and R. Ruzziconi,Superboost transitions, refraction memory and super-Lorentz charge algebra, JHEP11(2018) 200 [1810.00377]. [Erratum: JHEP 04, 172 (2020)]

2018 arXiv
[37]

Freidel, R

L. Freidel, R. Oliveri, D. Pranzetti and S. Speziale,The Weyl BMS group and Einstein ’s equations, JHEP07(2021) 170 [2104.05793]

2021 arXiv
[38]

McNees and C

R. McNees and C. Zwikel,The symplectic potential for leaky boundaries, JHEP01(2025) 049 [2408.13203]

2025
[39]

Campiglia and J

M. Campiglia and J. Peraza,Generalized BMS charge algebra, Phys. Rev. D101(2020), no. 10 104039 [2002.06691]

2020 arXiv
[40]

Rignon-Bret and S

A. Rignon-Bret and S. Speziale,Centerless BMS charge algebra, Phys. Rev. D110(2024), no. 4 044050 [2405.01526]

2024 arXiv
[41]

I. M. Anderson and C. G. Torre,Asymptotic conservation laws in field theory, Phys. Rev. Lett. 77(1996) 4109–4113 [hep-th/9608008]

1996 arXiv
[42]

Chandrasekaran, E

V. Chandrasekaran, E. E. Flanagan and K. Prabhu,Symmetries and charges of general relativity at null boundaries, JHEP11(2018) 125 [1807.11499]

2018 arXiv
[43]

Holst,Barbero’s Hamiltonian derived from a generalized Hilbert-Palatini action, Phys

S. Holst,Barbero’s Hamiltonian derived from a generalized Hilbert-Palatini action, Phys. Rev. D53(1996) 5966–5969 [gr-qc/9511026]

1996 arXiv
[44]

Godazgar, M

H. Godazgar, M. Godazgar and C. N. Pope,New dual gravitational charges, Phys. Rev. D99 (2019), no. 2 024013 [1812.01641]

2019 arXiv
[45]

Godazgar, M

H. Godazgar, M. Godazgar and M. J. Perry,Hamiltonian derivation of dual gravitational charges, JHEP09(2020) 084 [2007.07144]. 65

2020 arXiv
[46]

Oliveri and S

R. Oliveri and S. Speziale,A note on dual gravitational charges, JHEP12(2020) 079 [2010.01111]

2020 arXiv
[47]

Strominger,Lectures on the Infrared Structure of Gravity and Gauge Theory,1703.05448

A. Strominger,Lectures on the Infrared Structure of Gravity and Gauge Theory,1703.05448

arXiv
[48]

Witten,Quantum Field Theory and the Jones Polynomial, Commun

E. Witten,Quantum Field Theory and the Jones Polynomial, Commun. Math. Phys.121 (1989) 351–399

1989
[49]

Carlip,The (2+1)-Dimensional black hole, Class

S. Carlip,The (2+1)-Dimensional black hole, Class. Quant. Grav.12(1995) 2853–2880 [gr-qc/9506079]

1995 arXiv
[50]

Gawedzki,Conformal field theory: A Case study,hep-th/9904145

K. Gawedzki,Conformal field theory: A Case study,hep-th/9904145

arXiv
[51]

Odak and S

G. Odak and S. Speziale,Brown-York charges with mixed boundary conditions, JHEP11 (2021) 224 [2109.02883]

2021 arXiv
[52]

Hopfm¨ uller and L

F. Hopfm¨ uller and L. Freidel,Null Conservation Laws for Gravity, Phys. Rev. D97(2018), no. 12 124029 [1802.06135]

2018 arXiv
[53]

Carrozza, S

S. Carrozza, S. Eccles and P. A. Hoehn,Edge modes as dynamical frames: charges from post-selection in generally covariant theories,2205.00913

arXiv
[54]

G. Odak, A. Rignon-Bret and S. Speziale,General gravitational charges on null hypersurfaces, JHEP12(2023) 038 [2309.03854]

2023 arXiv
[55]

Rignon-Bret and S

A. Rignon-Bret and S. Speziale,Spatially local energy density of gravitational waves, JHEP03 (2025) 048 [2405.08808]

2025 arXiv
[56]

Brown, S

J. Brown, S. Lau and J. York,Action and energy of the gravitational field, Annals of Physics 297(2002), no. 2 175–218 [gr–qc/0010024]

2002
[57]

Lehner, R

L. Lehner, R. C. Myers, E. Poisson and R. D. Sorkin,Gravitational action with null boundaries, Phys. Rev. D94(2016), no. 8 084046 [1609.00207]

2016 arXiv
[58]

York,Boundary terms in the action principles of general relativity, Found

J. York,Boundary terms in the action principles of general relativity, Found. Phys.16(1986) 249–257

1986
[59]

An and M

Z. An and M. T. Anderson,The initial boundary value problem and quasi-local Hamiltonians in General Relativity,2103.15673

arXiv
[60]

An and M

Z. An and M. T. Anderson,Well-posed geometric boundary data in General Relativity, I: Conformal-mean curvature boundary data,2503.12599

arXiv
[61]

Anninos, D

D. Anninos, D. A. Galante and C. Maneerat,Gravitational observatories, JHEP12(2023) 024 [2310.08648]

2023 arXiv
[62]

Anninos, R

D. Anninos, R. Arias, D. A. Galante and C. Maneerat,Gravitational observatories in AdS 4, JHEP07(2025) 234 [2412.16305]

2025 arXiv
[63]

D. A. Galante, C. Maneerat and A. Svesko,Conformal boundaries near extremal black holes, Class. Quant. Grav.42(2025), no. 19 195003 [2504.14003]. 66

2025
[64]

X. Liu, H. S. Reall, J. E. Santos and T. Wiseman,Ill-posedness of the Cauchy problem for linearized gravity in a cavity with conformal boundary conditions, Class. Quant. Grav.42 (2025), no. 23 235003 [2505.20410]

2025 arXiv
[65]

D. A. Galante, R. C. Myers and T. Zikopoulos,Conformal Boundary Conditions and Higher Curvature Gravity,2512.10930
[66]

J. D. Brown and J. W. York, Jr.,Quasilocal energy and conserved charges derived from the gravitational action, Phys. Rev. D47(1993) 1407–1419 [gr-qc/9209012]

1993 arXiv
[67]

R. M. Wald,General relativity. University of Chicago press, 2010

2010
[68]

Ashtekar, C

A. Ashtekar, C. Beetle, O. Dreyer, S. Fairhurst, B. Krishnan, J. Lewandowski and J. Wisniewski,Isolated horizons and their applications, Phys. Rev. Lett.85(2000) 3564–3567 [gr-qc/0006006]

2000 arXiv
[69]

Ashtekar, S

A. Ashtekar, S. Fairhurst and B. Krishnan,Isolated horizons: Hamiltonian evolution and the first law, Phys. Rev. D62(2000) 104025 [gr-qc/0005083]

2000 arXiv
[70]

Ashtekar and B

A. Ashtekar and B. Krishnan,Isolated and dynamical horizons and their applications, Living Rev. Rel.7(2004) 10 [gr-qc/0407042]

2004 arXiv
[71]

H´ ajiˇ cek,Exact models of charged black holes, Communications in Mathematical Physics34 (1973), no

P. H´ ajiˇ cek,Exact models of charged black holes, Communications in Mathematical Physics34 (1973), no. 1 53–76

1973
[72]

Newman and R

E. Newman and R. Penrose,An approach to gravitational radiation by a method of spin coefficients, J.Math.Phys.3(1962) 566–578

1962
[73]

Booth and S

I. Booth and S. Fairhurst,Isolated, slowly evolving, and dynamical trapping horizons: Geometry and mechanics from surface deformations, Phys. Rev. D75(2007) 084019 [gr-qc/0610032]

2007 arXiv
[74]

Ashtekar and S

A. Ashtekar and S. Speziale,Null infinity as a weakly isolated horizon, Phys. Rev. D110 (2024), no. 4 044048 [2402.17977]

2024 arXiv
[75]

Ciambelli, R

L. Ciambelli, R. G. Leigh, C. Marteau and P. M. Petropoulos,Carroll Structures, Null Geometry and Conformal Isometries, Phys. Rev. D100(2019), no. 4 046010 [1905.02221]

2019 arXiv
[76]

Herfray,Carrollian manifolds and null infinity: a view from Cartan geometry, Class

Y. Herfray,Carrollian manifolds and null infinity: a view from Cartan geometry, Class. Quant. Grav.39(2022), no. 21 215005 [2112.09048]

2022 arXiv
[77]

Fiorucci, S

A. Fiorucci, S. Pekar, P. Marios Petropoulos and M. Vilatte,Carrollian-holographic Derivation of BMS Flux-balance Laws,2505.00077
[78]

Ciambelli and P

L. Ciambelli and P. Jai-akson,Foundations of Carrollian Geometry,2510.21651

arXiv
[79]

Parattu, S

K. Parattu, S. Chakraborty, B. R. Majhi and T. Padmanabhan,A Boundary Term for the Gravitational Action with Null Boundaries, Gen. Rel. Grav.48(2016), no. 7 94 [1501.01053]

2016 arXiv
[80]

Hopfm¨ uller and L

F. Hopfm¨ uller and L. Freidel,Gravity Degrees of Freedom on a Null Surface, Phys. Rev. D95 (2017), no. 10 104006 [1611.03096]. 67

2017 arXiv
[81]

Alexandrov and S

S. Alexandrov and S. Speziale,First order gravity on the light front, Phys. Rev. D91(2015), no. 6 064043 [1412.6057]

2015 arXiv
[82]

Chandrasekhar,The mathematical theory of black holes

S. Chandrasekhar,The mathematical theory of black holes. Claredon, Oxford UK, 1985

1985
[83]

Ciambelli, L

L. Ciambelli, L. Freidel and R. G. Leigh,Null Raychaudhuri: canonical structure and the dressing time, JHEP01(2024) 166 [2309.03932]

2024 arXiv
[84]

R. M. Wald,Black hole entropy is the Noether charge, Phys. Rev. D48(1993), no. 8 R3427–R3431 [gr-qc/9307038]

1993 arXiv
[85]

Chandrasekaran and K

V. Chandrasekaran and K. Prabhu,Symmetries, charges and conservation laws at causal diamonds in general relativity, JHEP10(2019) 229 [1908.00017]

2019 arXiv
[86]

Rignon-Bret,Second law from the Noether current on null hypersurfaces, Phys

A. Rignon-Bret,Second law from the Noether current on null hypersurfaces, Phys. Rev. D108 (2023), no. 4 044069 [2303.07262]

2023 arXiv
[87]

Hollands, R

S. Hollands, R. M. Wald and V. G. Zhang,Entropy of dynamical black holes, Phys. Rev. D 110(2024), no. 2 024070 [2402.00818]

2024 arXiv
[88]

Rignon-Bret,Black hole thermodynamic potentials for asymptotic observers, Phys

A. Rignon-Bret,Black hole thermodynamic potentials for asymptotic observers, Phys. Rev. D 110(2024), no. 12 124002 [2406.15843]

2024 arXiv
[89]

Ashtekar, J

A. Ashtekar, J. Engle, T. Pawlowski and C. Van Den Broeck,Multipole moments of isolated horizons, Class. Quant. Grav.21(2004) 2549–2570 [gr-qc/0401114]

2004 arXiv
[90]

Ashtekar, N

A. Ashtekar, N. Khera, M. Kolanowski and J. Lewandowski,Non-expanding horizons: multipoles and the symmetry group, JHEP01(2022) 028 [2111.07873]

2022 arXiv
[91]

A. C. Wall,A Second Law for Higher Curvature Gravity, Int. J. Mod. Phys. D24(2015), no. 12 1544014 [1504.08040]

2015 arXiv
[92]

Ashtekar, N

A. Ashtekar, N. Khera, M. Kolanowski and J. Lewandowski,Charges and fluxes on (perturbed) non-expanding horizons, JHEP02(2022) 066 [2112.05608]

2022 arXiv
[93]

M. R. Visser and Z. Yan,Properties of dynamical black hole entropy, JHEP10(2024) 029 [2403.07140]

2024 arXiv
[94]

Donnay, G

L. Donnay, G. Giribet, H. A. Gonzalez and M. Pino,Supertranslations and Superrotations at the Black Hole Horizon, Phys. Rev. Lett.116(2016), no. 9 091101 [1511.08687]

2016 arXiv
[95]

Donnay, G

L. Donnay, G. Giribet, H. A. Gonz´ alez and M. Pino,Extended Symmetries at the Black Hole Horizon, JHEP09(2016) 100 [1607.05703]

2016 arXiv
[96]

Adami, D

H. Adami, D. Grumiller, S. Sadeghian, M. M. Sheikh-Jabbari and C. Zwikel,T-Witts from the horizon, JHEP04(2020) 128 [2002.08346]

2020 arXiv
[97]

Adami, M

H. Adami, M. M. Sheikh-Jabbari, V. Taghiloo and H. Yavartanoo,Null surface thermodynamics, Phys. Rev. D105(2022), no. 6 066004 [2110.04224]

2022 arXiv
[98]

Ashtekar and S

A. Ashtekar and S. Speziale,Horizons and null infinity: A fugue in four voices, Phys. Rev. D 109(2024), no. 6 L061501 [2401.15618]. 68

2024 arXiv
[99]

Bondi,Gravitational Waves in General Relativity, Nature186(1960), no

H. Bondi,Gravitational Waves in General Relativity, Nature186(1960), no. 4724 535–535

1960
[100]

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

1962
[101]

Penrose,Conformal treatment of infinity,

R. Penrose,Conformal treatment of infinity,
[102]

Ashtekar and R

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

1978
[103]

De Paoli and S

E. De Paoli and S. Speziale,Sachs free data in real connection variables, JHEP11(2017) 205 [1707.00667]

2017 arXiv
[104]

Geiller and C

M. Geiller and C. Zwikel,The partial Bondi gauge: Further enlarging the asymptotic structure of gravity, SciPost Phys.13(2022) 108 [2205.11401]

2022 arXiv
[105]

Geiller and C

M. Geiller and C. Zwikel,The partial Bondi gauge: Gauge fixings and asymptotic charges, SciPost Phys.16(2024) 076 [2401.09540]

2024 arXiv
[106]

Barnich and C

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

2010 arXiv
[107]

Barnich and A

G. Barnich and A. Seraj,to appear,
[108]

Comp` ere, R

G. Comp` ere, R. Oliveri and A. Seraj,The Poincar´ e and BMS flux-balance laws with application to binary systems, JHEP10(2020) 116 [1912.03164]

2020 arXiv
[109]

E. E. Flanagan and D. A. Nichols,Conserved charges of the extended Bondi-Metzner-Sachs algebra, Phys. Rev. D95(2017), no. 4 044002 [1510.03386]

2017 arXiv
[110]

Ashtekar,Asymptotic quantization : based on 1984 Naples lectures / Abhay Ashtekar

A. Ashtekar,Asymptotic quantization : based on 1984 Naples lectures / Abhay Ashtekar. Monographs and textbooks in physical science. Bibliopolis, Napoli, 1987

1984
[111]

A. M. Grant, K. Prabhu and I. Shehzad,The Wald-Zoupas prescription for asymptotic charges at null infinity in general relativity, Class. Quant. Grav.39(2022), no. 8 085002 [2105.05919]

2022 arXiv
[112]

Donnay, K

L. Donnay, K. Nguyen and R. Ruzziconi,Loop-corrected subleading soft theorem and the celestial stress tensor, JHEP09(2022) 063 [2205.11477]

2022 arXiv
[113]

Bondi, M

H. Bondi, M. G. J. van der Burg and A. W. K. Metzner,Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems, Proc. Roy. Soc. Lond.A269(1962) 21–52

1962
[114]

E. T. Newman and R. Penrose,Note on the Bondi-Metzner-Sachs group, J. Math. Phys.7 (1966) 863–870

1966
[115]

Barnich and P.-H

G. Barnich and P.-H. Lambert,A Note on the Newman-Unti group and the BMS charge algebra in terms of Newman-Penrose coefficients, Adv. Math. Phys.2012(2012) 197385 [1102.0589]

2012 arXiv
[116]

Ashtekar,Geometry and Physics of Null Infinity,1409.1800

A. Ashtekar,Geometry and Physics of Null Infinity,1409.1800. 69

arXiv
[117]

Barnich,Centrally extended BMS4 Lie algebroid, JHEP06(2017) 007 [1703.08704]

G. Barnich,Centrally extended BMS4 Lie algebroid, JHEP06(2017) 007 [1703.08704]

2017 arXiv
[118]

Barnich, P

G. Barnich, P. Mao and R. Ruzziconi,BMS current algebra in the context of the Newman-Penrose formalism, Class. Quant. Grav.37(2020), no. 9 095010 [1910.14588]

2020 arXiv
[119]

Barnich and R

G. Barnich and R. Ruzziconi,Coadjoint representation of the BMS group on celestial Riemann surfaces, JHEP06(2021) 079 [2103.11253]

2021 arXiv
[120]

Barnich, K

G. Barnich, K. Nguyen and R. Ruzziconi,Geometric action for extended Bondi-Metzner-Sachs group in four dimensions, JHEP12(2022) 154 [2211.07592]

2022 arXiv
[121]

Prabhu,Conservation of asymptotic charges from past to future null infinity: Supermomentum in general relativity, JHEP03(2019) 148 [1902.08200]

K. Prabhu,Conservation of asymptotic charges from past to future null infinity: Supermomentum in general relativity, JHEP03(2019) 148 [1902.08200]

2019 arXiv
[122]

Prabhu and I

K. Prabhu and I. Shehzad,Conservation of asymptotic charges from past to future null infinity: Lorentz charges in general relativity, JHEP08(2022) 029 [2110.04900]

2022 arXiv
[123]

Capone, K

F. Capone, K. Nguyen and E. Parisini,Charge and antipodal matching across spatial infinity, SciPost Phys.14(2023), no. 2 014 [2204.06571]

2023 arXiv
[124]

Strominger,Asymptotic Symmetries of Yang-Mills Theory, JHEP07(2014) 151 [1308.0589]

A. Strominger,Asymptotic Symmetries of Yang-Mills Theory, JHEP07(2014) 151 [1308.0589]

2014 arXiv
[125]

Strominger,On BMS Invariance of Gravitational Scattering, JHEP07(2014) 152 [1312.2229]

A. Strominger,On BMS Invariance of Gravitational Scattering, JHEP07(2014) 152 [1312.2229]

2014 arXiv
[126]

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

2015 arXiv
[127]

Kapec, V

D. Kapec, V. Lysov, S. Pasterski and A. Strominger,Semiclassical Virasoro symmetry of the quantum gravityS-matrix, JHEP08(2014) 058 [1406.3312]

2014 arXiv
[128]

Kapec, P

D. Kapec, P. Mitra, A.-M. Raclariu and A. Strominger,2D Stress Tensor for 4D Gravity, Phys. Rev. Lett.119(2017), no. 12 121601 [1609.00282]

2017 arXiv
[129]

Campiglia and A

M. Campiglia and A. Laddha,Asymptotic symmetries and subleading soft graviton theorem, Phys. Rev. D90(2014), no. 12 124028 [1408.2228]

2014 arXiv
[130]

S. Choi, A. Laddha and A. Puhm,Asymptotic Symmetries for Logarithmic Soft Theorems in Gauge Theory and Gravity,2403.13053

arXiv
[131]

Barnich and C

G. Barnich and C. Troessaert,Finite BMS transformations, JHEP03(2016) 167 [1601.04090]

2016 arXiv
[132]

Comp` ere, A

G. Comp` ere, A. Fiorucci and R. Ruzziconi,TheΛ-BMS 4 charge algebra, JHEP10(2020) 205 [2004.10769]

2020 arXiv
[133]

Campiglia and A

M. Campiglia and A. Laddha,BMS Algebra, Double Soft Theorems, and All That,2106.14717

arXiv
[134]

Satishchandran and R

G. Satishchandran and R. M. Wald,Asymptotic behavior of massless fields and the memory effect, Phys. Rev. D99(2019), no. 8 084007 [1901.05942]

2019 arXiv
[135]

E. E. Flanagan and D. A. Nichols,Fully nonlinear transformations of the Weyl-Bondi-Metzner-Sachs asymptotic symmetry group,2311.03130. 70

arXiv
[136]

Geiller,Celestialw 1+∞ charges and the subleading structure of asymptotically-flat spacetimes,2403.05195

M. Geiller,Celestialw 1+∞ charges and the subleading structure of asymptotically-flat spacetimes,2403.05195

arXiv
[137]

Freidel, D

L. Freidel, D. Pranzetti and A.-M. Raclariu,Higher spin dynamics in gravity and w1+∞ celestial symmetries, Phys. Rev. D106(2022), no. 8 086013 [2112.15573]

2022 arXiv
[138]

Donnay, A

L. Donnay, A. Fiorucci, Y. Herfray and R. Ruzziconi,Bridging Carrollian and Celestial Holography,2212.12553

arXiv
[139]

Capone,General null asymptotics and superrotation-compatible configuration spaces in d≥4, JHEP10(2021) 158 [2108.01203]

F. Capone,General null asymptotics and superrotation-compatible configuration spaces in d≥4, JHEP10(2021) 158 [2108.01203]. [Erratum: JHEP 02, 113 (2022)]

2021 arXiv
[140]

A. Kmec, L. Mason, R. Ruzziconi and A. Yelleshpur Srikant,CelestialLw 1+∞ charges from a twistor action, JHEP10(2024) 250 [2407.04028]

2024 arXiv
[141]

Pranzetti and D

D. Pranzetti and D. G. Salluce,Double-soft limit and celestial shadow OPE from charge bracket,2510.26520
[142]

Geiller, P

M. Geiller, P. Mao and A. Vincenti,Twisting asymptotically-flat spacetimes,2511.13814

arXiv
[143]

Cresto and L

N. Cresto and L. Freidel,Asymptotic higher spin symmetries I: covariant wedge algebra in gravity, Lett. Math. Phys.115(2025), no. 2 39 [2409.12178]

2025 arXiv
[144]

Godazgar, M

H. Godazgar, M. Godazgar and C. N. Pope,Subleading BMS charges and fake news near null infinity, JHEP01(2019) 143 [1809.09076]

2019 arXiv
[145]

Godazgar, M

H. Godazgar, M. Godazgar and C. Pope,Dual gravitational charges and soft theorems, JHEP 10(2019) 123 [1908.01164]

2019 arXiv
[146]

Godazgar and G

M. Godazgar and G. Long,Higher derivative asymptotic charges and internal Lorentz symmetries, Phys. Rev. D105(2022), no. 8 084037 [2201.07014]

2022 arXiv
[147]

Godazgar, G

M. Godazgar, G. Long and A. Seraj,Gravitational memory effects and higher derivative actions, JHEP09(2022) 150 [2206.12339]

2022 arXiv
[148]

J. L. V. Cerdeira and T. Ort ´ ın,On-shell Lagrangians as total derivatives and the generalized Komar charge, JHEP09(2025) 068 [2506.14024]

2025 arXiv
[149]

G´ omez-Fayr´ en, P

C. G´ omez-Fayr´ en, P. Meessen and T. Ort ´ ın,Covariant generalized conserved charges of General Relativity, JHEP09(2023) 174 [2307.04041]

2023 arXiv
[150]

Ortin and D

T. Ortin and D. Pere˜ niguez,Magnetic charges and Wald entropy, JHEP11(2022) 081 [2207.12008]

2022 arXiv
[151]

Bandos and T

I. Bandos and T. Ortin,Noether-Wald charge in supergravity: the fermionic contribution, JHEP12(2023) 095 [2305.10617]

2023 arXiv
[152]

Mittal, P

N. Mittal, P. M. Petropoulos, D. Rivera-Betancour and M. Vilatte,Ehlers, Carroll, charges and dual charges, JHEP07(2023) 065 [2212.14062]

2023 arXiv
[153]

Gao,The First law of black hole mechanics in Einstein-Maxwell and Einstein-Yang-Mills theories, Phys

S. Gao,The First law of black hole mechanics in Einstein-Maxwell and Einstein-Yang-Mills theories, Phys. Rev. D68(2003) 044016 [gr-qc/0304094]. 71

2003 arXiv
[154]

Mars and J

M. Mars and J. M. M. Senovilla,Trapped surfaces and symmetries, Class. Quant. Grav.20 (2003) L293–L300 [gr-qc/0309055]

2003 arXiv
[155]

Ashtekar, M

A. Ashtekar, M. Campiglia and S. Shah,Dynamical Black Holes: Approach to the Final State, Phys. Rev. D88(2013), no. 6 064045 [1306.5697]

2013 arXiv
[156]

Donnay, G

L. Donnay, G. Giribet, H. A. Gonz´ alez and A. Puhm,Black hole memory effect, Phys. Rev. D 98(2018), no. 12 124016 [1809.07266]

2018 arXiv
[157]

Rignon-Bret,Note on the physical process first law of black hole mechanics, Phys

A. Rignon-Bret,Note on the physical process first law of black hole mechanics, Phys. Rev. D 108(2023), no. 2 024005 [2303.06731]

2023 arXiv
[158]

A. C. Wall and Z. Yan,Linearized second law for higher curvature gravity and nonminimally coupled vector fields, Phys. Rev. D110(2024), no. 8 084005 [2402.05411]

2024 arXiv
[159]

Hajian and M

K. Hajian and M. Sheikh-Jabbari,Solution Phase Space and Conserved Charges: A General Formulation for Charges Associated with Exact Symmetries, Phys. Rev. D93(2016), no. 4 044074 [1512.05584]

2016 arXiv
[160]

Adami, D

H. Adami, D. Grumiller, M. M. Sheikh-Jabbari, V. Taghiloo, H. Yavartanoo and C. Zwikel, Null boundary phase space: slicings, news & memory, JHEP11(2021) 155 [2110.04218]

2021 arXiv
[161]

Ciambelli, C

L. Ciambelli, C. Marteau, A. C. Petkou, P. M. Petropoulos and K. Siampos,Flat holography and Carrollian fluids, JHEP07(2018) 165 [1802.06809]

2018 arXiv
[162]

Ciambelli, C

L. Ciambelli, C. Marteau, A. C. Petkou, P. M. Petropoulos and K. Siampos,Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids, Class. Quant. Grav.35 (2018), no. 16 165001 [1802.05286]

2018 arXiv
[163]

H. R. Safari and M. M. Sheikh-Jabbari,BMS 4 algebra, its stability and deformations, JHEP04 (2019) 068 [1902.03260]

2019 arXiv
[164]

Ciambelli and R

L. Ciambelli and R. G. Leigh,Weyl Connections and their Role in Holography, Phys. Rev. D 101(2020), no. 8 086020 [1905.04339]

2020 arXiv
[165]

Ciambelli and R

L. Ciambelli and R. G. Leigh,Isolated surfaces and symmetries of gravity, Phys. Rev. D104 (2021), no. 4 046005 [2104.07643]

2021 arXiv
[166]

Ciambelli,From Asymptotic Symmetries to the Corner Proposal, PoSModave2022(2023) 002 [2212.13644]

L. Ciambelli,From Asymptotic Symmetries to the Corner Proposal, PoSModave2022(2023) 002 [2212.13644]

2023 arXiv
[167]

A. J. Speranza,Ambiguity resolution for integrable gravitational charges, JHEP07(2022) 029 [2202.00133]

2022 arXiv
[168]

Ciambelli and R

L. Ciambelli and R. G. Leigh,Universal corner symmetry and the orbit method for gravity, Nucl. Phys. B986(2023) 116053 [2207.06441]

2023 arXiv
[169]

Donnay, A

L. Donnay, A. Fiorucci, Y. Herfray and R. Ruzziconi,Carrollian Perspective on Celestial Holography, Phys. Rev. Lett.129(2022), no. 7 071602 [2202.04702]

2022 arXiv
[170]

Adami, A

H. Adami, A. Parvizi, M. M. Sheikh-Jabbari, V. Taghiloo and H. Yavartanoo,Carrollian structure of the null boundary solution space, JHEP02(2024) 073 [2311.03515]. 72

2024 arXiv
[171]

V. R. Shajiee and M. M. Sheikh-Jabbari,A New Derivation of Classical Gravitational Second Law of Thermodynamics,2511.07510
[172]

Ruzziconi and C

R. Ruzziconi and C. Zwikel,CelestialLw 1+∞ Symmetries and Subleading Phase Space of Null Hypersurfaces,2511.07525
[173]

Agrawal, P

S. Agrawal, P. Charalambous and L. Donnay,Null infinity as an inverted extremal horizon: Matching an infinite set of conserved quantities for gravitational perturbations,2506.15526
[174]

Parvizi, M

A. Parvizi, M. M. Sheikh-Jabbari and V. Taghiloo,Freelance holography, part I: Setting boundary conditions free in gauge/gravity correspondence, SciPost Phys.19(2025), no. 2 043 [2503.09371]

2025 arXiv
[175]

Parvizi, M

A. Parvizi, M. M. Sheikh-Jabbari and V. Taghiloo,Freelance Holography, Part II: Moving Boundary in Gauge/Gravity Correspondence, SciPost Phys. Core8(2025) 075 [2503.09372]

2025
[176]

Ortin,A Note on Lie-Lorentz derivatives, Class

T. Ortin,A Note on Lie-Lorentz derivatives, Class. Quant. Grav.19(2002) L143–L150 [hep-th/0206159]

2002 arXiv
[177]

Ashtekar, J

A. Ashtekar, J. Engle and D. Sloan,Asymptotics and Hamiltonians in a First order formalism, Class. Quant. Grav.25(2008) 095020 [0802.2527]

2008 arXiv
[178]

Corichi and E

A. Corichi and E. Wilson-Ewing,Surface terms, Asymptotics and Thermodynamics of the Holst Action, Class. Quant. Grav.27(2010) 205015 [1005.3298]

2010 arXiv
[179]

Corichi, I

A. Corichi, I. Rubalcava and T. Vukasinac,Hamiltonian and Noether charges in first order gravity, Gen. Rel. Grav.46(2014) 1813 [1312.7828]

2014 arXiv
[180]

Jacobson and A

T. Jacobson and A. Mohd,Black hole entropy and Lorentz-diffeomorphism Noether charge, Phys. Rev. D92(2015) 124010 [1507.01054]

2015 arXiv
[181]

Prabhu,The First Law of Black Hole Mechanics for Fields with Internal Gauge Freedom, Class

K. Prabhu,The First Law of Black Hole Mechanics for Fields with Internal Gauge Freedom, Class. Quant. Grav.34(2017), no. 3 035011 [1511.00388]

2017 arXiv
[182]

Corichi and J

A. Corichi and J. D. Reyes,The gravitational Hamiltonian, first order action, Poincar´ e charges and surface terms, Class. Quant. Grav.32(2015), no. 19 195024 [1505.01518]

2015 arXiv
[183]

Corichi, I

A. Corichi, I. Rubalcava-Garc ´ ıa and T. Vukaˇ sinac,Actions, topological terms and boundaries in first-order gravity: A review, Int. J. Mod. Phys. D25(2016), no. 04 1630011 [1604.07764]

2016 arXiv
[184]

Barnich, P

G. Barnich, P. Mao and R. Ruzziconi,Conserved currents in the Cartan formulation of general relativity, inAbout Various Kinds of Interactions: Workshop in honour of Professor Philippe Spindel Mons, Belgium, June 4-5, 2015, 2016.1611.01777

2015
[185]

Frodden and D

E. Frodden and D. Hidalgo,Surface Charges for Gravity and Electromagnetism in the First Order Formalism, Class. Quant. Grav.35(2018), no. 3 035002 [1703.10120]

2018 arXiv
[186]

J. F. B. G., J. Margalef-Bentabol, V. Varo and E. J. S. Villase˜ nor,Covariant phase space for gravity with boundaries: Metric versus tetrad formulations, Phys. Rev. D104(2021), no. 4 044048 [2103.06362]. 73

2021 arXiv
[187]

A. S. Cattaneo and M. Schiavina,BV-BFV approach to General Relativity, Einstein-Hilbert action, J. Math. Phys.57(2016), no. 2 023515 [1509.05762]

2016 arXiv
[188]

Canepa, A

G. Canepa, A. S. Cattaneo and M. Schiavina,Boundary structure of general relativity in tetrad variables, Adv. Theor. Math. Phys.25(2021), no. 2 327–377 [2001.11004]

2021 arXiv
[189]

Hadfield, S

C. Hadfield, S. Kandel and M. Schiavina,Ruelle zeta function from field theory, Annales Henri Poincare21(2020), no. 12 3835–3867 [2002.03952]

2020 arXiv
[190]

F. M. C. Sim˜ ao, A. S. Cattaneo and M. Schiavina,BV equivalence with boundary, Lett. Math. Phys.113(2023), no. 1 25 [2109.05268]

2023 arXiv
[191]

Riello and M

A. Riello and M. Schiavina,Hamiltonian gauge theory with corners: constraint reduction and flux superselection,2207.00568

arXiv
[192]

A. S. Cattaneo, P. Mnev and M. Schiavina,BV Quantization,2307.07761

arXiv
[193]

Riello and M

A. Riello and M. Schiavina,Phase spaces in field theory: Reduction vs. resolution,2509.24450
[194]

Baulieu, L

L. Baulieu, L. Ciambelli and T. Wetzstein,Extended-BMS Anomalies and Flat Space Holography,2504.10304

arXiv
[195]

Baulieu and T

L. Baulieu and T. Wetzstein,BRST covariant phase space and holographic Ward identities, JHEP10(2024) 055 [2405.18898]

2024 arXiv
[196]

Comp` ere, R

G. Comp` ere, R. Oliveri and A. Seraj,Gravitational multipole moments from Noether charges, JHEP05(2018) 054 [1711.08806]

2018 arXiv
[197]

Hosseinzadeh, A

V. Hosseinzadeh, A. Seraj and M. Sheikh-Jabbari,Soft Charges and Electric-Magnetic Duality, JHEP08(2018) 102 [1806.01901]

2018 arXiv
[198]

Blanchet, G

L. Blanchet, G. Comp` ere, G. Faye, R. Oliveri and A. Seraj,Multipole expansion of gravitational waves: from harmonic to Bondi coordinates, JHEP02(2021) 029 [2011.10000]

2021 arXiv
[199]

Seraj,Gravitational breathing memory and dual symmetries, JHEP05(2021) 283 [2103.12185]

A. Seraj,Gravitational breathing memory and dual symmetries, JHEP05(2021) 283 [2103.12185]

2021 arXiv
[200]

Seraj and B

A. Seraj and B. Oblak,Gyroscopic gravitational memory, JHEP11(2023) 057 [2112.04535]

2023 arXiv
[201]

Seraj and B

A. Seraj and B. Oblak,Precession Caused by Gravitational Waves, Phys. Rev. Lett.129 (2022), no. 6 061101 [2203.16216]

2022 arXiv
[202]

Donnay, A

L. Donnay, A. Puhm and A. Strominger,Conformally Soft Photons and Gravitons, JHEP01 (2019) 184 [1810.05219]

2019 arXiv
[203]

Donnay, S

L. Donnay, S. Pasterski and A. Puhm,Asymptotic Symmetries and Celestial CFT, JHEP09 (2020) 176 [2005.08990]

2020 arXiv
[204]

Campoleoni, L

A. Campoleoni, L. Ciambelli, A. Delfante, C. Marteau, P. M. Petropoulos and R. Ruzziconi, Holographic Lorentz and Carroll frames, JHEP12(2022) 007 [2208.07575]

2022 arXiv
[205]

Campoleoni, A

A. Campoleoni, A. Delfante, S. Pekar, P. M. Petropoulos, D. Rivera-Betancour and M. Vilatte, Flat from anti de Sitter, JHEP12(2023) 078 [2309.15182]. 74

2023 arXiv
[206]

Fiorucci, D

A. Fiorucci, D. Grumiller and R. Ruzziconi,Logarithmic celestial conformal field theory, Phys. Rev. D109(2024), no. 2 L021902 [2305.08913]

2024 arXiv
[207]

Campoleoni, D

A. Campoleoni, D. Francia and C. Heissenberg,On higher-spin supertranslations and superrotations, JHEP05(2017) 120 [1703.01351]

2017 arXiv
[208]

Campoleoni, D

A. Campoleoni, D. Francia and C. Heissenberg,Asymptotic Charges at Null Infinity in Any Dimension, Universe4(2018), no. 3 47 [1712.09591]

2018 arXiv
[209]

Francia and C

D. Francia and C. Heissenberg,Two-Form Asymptotic Symmetries and Scalar Soft Theorems, Phys. Rev. D98(2018), no. 10 105003 [1810.05634]

2018 arXiv
[210]

Campoleoni, D

A. Campoleoni, D. Francia and C. Heissenberg,On asymptotic symmetries in higher dimensions for any spin, JHEP12(2020) 129 [2011.04420]

2020 arXiv
[211]

Francia and F

D. Francia and F. Manzoni,Asymptotic charges ofp−forms and their dualities in anyD, 2411.04926

arXiv
[212]

Campoleoni, A

A. Campoleoni, A. Delfante, D. Francia and C. Heissenberg,Finite actions and asymptotic charges at null infinity for any spin, Phys. Lett. B870(2025) 139908 [2507.19310]. 75

2025

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

[1] [1]

Geroch,Asymptotic Structure of Space-Time, ch

R. Geroch,Asymptotic Structure of Space-Time, ch. 1, pp. 1–106. Springer US, Boston, MA, 1977

1977

[2] [2]

Ashtekar,Radiative Degrees of Freedom of the Gravitational Field in Exact General Relativity, J

A. Ashtekar,Radiative Degrees of Freedom of the Gravitational Field in Exact General Relativity, J. Math. Phys.22(1981) 2885–2895

1981

[3] [3]

Ashtekar and M

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

1981

[4] [4]

Dray and M

T. Dray and M. Streubel,Angular momentum at null infinity, Class. Quant. Grav.1(1984), no. 1 15–26

1984

[5] [5]

Dray,Momentum Flux At Null Infinity, Class

T. Dray,Momentum Flux At Null Infinity, Class. Quant. Grav.2(1985) L7–L10

1985

[6] [6]

R. M. Wald and A. Zoupas,A General definition of ’conserved quantities’ in general relativity and other theories of gravity, Phys. Rev. D61(2000) 084027 [gr-qc/9911095]

arXiv 2000

[7] [7]

Ashtekar and S

A. Ashtekar and S. Speziale,Null infinity and horizons: A new approach to fluxes and charges, Phys. Rev. D110(2024), no. 4 044049 [2407.03254]

arXiv 2024

[8] [8]

I. M. Anderson,Introduction to the variational bicomplex, bz Contemporary Mathematics132 (1992)

1992