Asymptotic symmetries and charges at spatial infinity in general relativity

Abstract

We analyze the asymptotic symmetries and their associated charges at spatial infinity in $4$-dimensional asymptotically-flat spacetimes. We use the covariant formalism of Ashtekar and Hansen where the asymptotic fields and symmetries live on the $3$-manifold of spatial directions at spatial infinity, represented by a timelike unit-hyperboloid (or de Sitter space). Using the covariant phase space formalism, we derive formulae for the charges corresponding to asymptotic supertranslations and Lorentz symmetries at spatial infinity. With the motivation of, eventually, proving that these charges match with those defined on null infinity -- as has been conjectured by Strominger -- we do not impose any restrictions on the choice of conformal factor in contrast to previous work on this problem. Since we work with a general conformal factor we expect that our charge expressions will be more suitable to prove the matching of the Lorentz charges at spatial infinity to those defined on null infinity, as has been recently shown for the supertranslation charges.

arXiv commentv2: 50 pages, typo in Eq. A.9 corrected, references updated, matches published version

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Cited by in corpus (14)

• The Holographic Nature of Null Infinity
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Conservation of asymptotic charges from past to future null infinity: Lorentz charges in general relativity
• The Wald-Zoupas prescription for asymptotic charges at null infinity in general relativity
• Asymptotic symmetries in spatially flat FRW
• BMS-supertranslation charges at the critical sets of null infinity
• Supertranslations at Timelike Infinity
• Celestial IR divergences and the effective action of supertranslation modes
• BMS Symmetry via AdS/CFT
• Higgs Phases and Boundary Criticality
• Calculation of asymptotic charges at the critical sets of null infinity
• Supertranslations at Spatial and Timelike Infinities in the First-Order Formalism
• Asymptotic charges for spin-1 and spin-2 fields at the critical sets of null infinity
• Gauge Invariant Propagators and States in Quantum Electrodynamics