Charge and antipodal matching across spatial infinity

Capone, Federico; Nguyen, Kévin; Parisini, Enrico

doi:10.21468/scipostphys.14.2.014

Cited by 15 publications

(8 citation statements)

References 81 publications

(234 reference statements)

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“…where we adopted a convention where one denotes X ℓ by ℓ. The last three terms can be rewritten as [P 3 (123). All in all we can rewrite the linear combination of fourth order 3-point invariants as…”

Section: Jhep05(2024)296mentioning

confidence: 99%

“…To help us answer this question, let us briefly present the Beig-Schmidt gauge [114,115], a suitable set of coordinates to describe the neighbourhood of past, future and spatial infinity. This gauge has been used to analyse the well-posedness of the variational principle at spatial infinity, and to define the scattering problem on general asymptotically flat spacetimes by studying BMS charges and their antipodal matching [116][117][118][119][120][121][122][123][124]. The geometry of a 4-dimensional Ricci-flat spacetime in a neighbourhood of spatial infinity can be written in Beig-Schmidt gauge as…”

Section: Relations With Flat Holographymentioning

confidence: 99%

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The ambient space formalism

Parisini,

Skenderis,

Withers

2024

J. High Energ. Phys.

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We present a new formalism to solve the kinematical constraints due to Weyl invariance for CFTs in curved backgrounds and/or non-trivial states, and we apply it to thermal CFTs and to CFTs on squashed spheres. The ambient space formalism is based on constructing a class of geometric objects that are Weyl covariant and identifying them as natural building blocks of correlation functions. We construct (scalar) n-point functions and we illustrate the formalism with a detailed computation of 2-point functions. We compare our results for thermal 2-point functions with results that follow from thermal OPEs and holographic computations, finding exact agreement. In our holographic computation we also obtain the OPE coefficient of the leading double-twist contribution, and we discuss how the double-twist coefficients may be computed from the multi-energy-momentum contributions, given knowledge of the analytic structure of the correlator. The 2-point function for the CFT on squashed spheres is a new result. We also discuss the relation of our work to flat holography.

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Section: Jhep05(2024)296mentioning

confidence: 99%

Section: Relations With Flat Holographymentioning

confidence: 99%

The ambient space formalism

Parisini,

Skenderis,

Withers

2024

J. High Energ. Phys.

Self Cite

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“…To make use of this gauge in the ECFEs, let ϕ denote an embedding map ϕ : S → M so that S is a submanifold of M and let φ denote the conformal transformation map φ : M → M so that the metric g ≡ Ξ 2 g on M satisfies eq. (32). Then, the map φ • ϕ : S → M is also an embedding so that S can be considered as a submanifold of M. If h is the metric induced by g on S and h is the metric induced by g on S, one has…”

Section: Hyperbolic Reduction Using the Conformal Gaussian Gaugementioning

confidence: 99%

“…Nevertheless, the covariant formulation of Ashtekar and Hansen [13] was used in [29,30] to prove the matching of asymptotic charges for the spin-1 and gravitational fields on spacetimes that satisfy Ashtekar-Hansen's notion of asymptotic flatness. Similar techniques were used in [31] to investigate the matching of Lorentz charges for the gravitational field on Ashtekar-Hansen asymptotically flat spacetimes -see also [32].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic charges for spin-1 and spin-2 fields at the critical sets of null infinity

Mohamed

Kroon

2022

Journal of Mathematical Physics

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The asymptotic charges of spin-1 and spin-2 fields are studied near spatial infinity. We evaluate the charges at the critical sets where spatial infinity meets null infinity with the aim of finding the relation between the charges at future and past null infinities. To this end, we make use of Friedrich’s framework of the cylinder at spatial infinity to obtain asymptotic expansions of the Maxwell and spin-2 fields near spatial infinity, which are fully determined in terms of initial data on a Cauchy hypersurface. With expanding the initial data in terms of spin-weighted spherical harmonics, it is shown that only a subset of the initial data, which satisfy certain regularity conditions, gives rise to well-defined charges at the point where future (past) infinity meets spatial infinity. Given such initial data, the charges are shown to be fully expressed in terms of the freely specifiable part of the data. Moreover, it is shown that there exists a natural correspondence between the charges defined at future and past null infinities.

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“…One significant challenge in this analysis is the singular nature of the conformal structure at spatial infinity i 0 , further highlighting the importance of the different representations of spatial infinity [5][6][7]25] in the discussion of the matching problem. In recent years, numerous articles discussed the asymptotic symmetry group at spatial infinity [26][27][28][29][30][31] and their matching with the asymptotic charges at null infinities [26,[32][33][34][35][36]. On Minkowski spacetime, the matching of supertranslation asymptotic charges has been investigated for the spin-1 field in [26] and the spin-2 field in [32].…”

Section: Introductionmentioning

confidence: 99%

Calculation of asymptotic charges at the critical sets of null infinity

Mohamed

2024

Phil. Trans. R. Soc. A.

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The asymptotic structure of null and spatial infinities of asymptotically flat spacetimes plays an essential role in discussing gravitational radiation, gravitational memory effect, and conserved quantities in General Relativity (GR). Bondi, Metzner and Sachs (BMS) established that the asymptotic symmetry group for asymptotically simple spacetimes is the infinite-dimensional BMS group. Given that null infinity is divided into two sets: past null infinity I − and future null infinity I + , one can identify two independent symmetry groups: BMS − at I − and BMS + at I + . Associated with these symmetries are the so-called BMS charges. A recent conjecture by Strominger suggests that the generators of BMS − and BMS + and their associated charges are related via an antipodal reflection map near spatial infinity. To verify this matching, an analysis of the gravitational field near spatial infinity is required. This task is complicated due to the singular nature of spatial infinity for spacetimes with non-vanishing ADM mass. Different frameworks have been introduced in the literature to address this singularity, e.g. Friedrich’s cylinder, Ashtekar-Hansen’s hyperboloid and Ashtekar-Romano’s asymptote at spatial infinity. This paper reviews the role of Friedrich’s formulation of spatial infinity in the investigation of the matching of the spin-2 charges on Minkowski spacetime and in the full GR setting. This article is part of a discussion meeting issue ‘At the interface of asymptotics, conformal methods and analysis in general relativity’.

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Charge and antipodal matching across spatial infinity

Cited by 15 publications

References 81 publications

The ambient space formalism

The ambient space formalism

Asymptotic charges for spin-1 and spin-2 fields at the critical sets of null infinity

Calculation of asymptotic charges at the critical sets of null infinity

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