Charge and Antipodal Matching across Spatial Infinity

Abstract

We derive the antipodal matching relations used to demonstrate the equivalence between soft graviton theorems and BMS charge conservation across spatial infinity. To this end we provide a precise map between Bondi data at null infinity $\mathcal{I}$ and Beig-Schmidt data at spatial infinity $i^0$ in a context appropriate to the gravitational scattering problem and celestial holography. In addition, we explicitly match the various proposals of BMS charges at $\mathcal{I}$ found in the literature with the conserved charges at $i^0$.

26 pages + appendices. v2: added references. v3: added references and comments. v4: corrected analysis for the antipodal matching of the angular momentum aspect, in agreement with recent observations made by Compere et al. in 2303.17124. v5: added funding acknowledgment

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• Evidence for a New Soft Graviton Theorem
• New symmetries for the Gravitational S-matrix
• Sub-subleading soft gravitons and large diffeomorphisms
• Covariant Counterterms and Conserved Charges in Asymptotically Flat Spacetimes
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Lectures on Celestial Holography
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• Multipole Expansion of Gravitational Waves: from Harmonic to Bondi coordinates
• On the Stress Tensor for Asymptotically Flat Gravity
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Cited by in corpus (12)

• Symmetries in Celestial CFT${}_d$
• Unified Treatment of null and Spatial Infinity IV: Angular Momentum at Null and Spatial Infinity
• BMS-supertranslation charges at the critical sets of null infinity
• Kac-Moody symmetry in the light front of gauge theories
• Unified Treatment of Null and Spatial Infinity III: Asymptotically Minkowski Space-times
• Electromagnetic multipole expansions and the logarithmic soft photon theorem
• Calculation of asymptotic charges at the critical sets of null infinity
• The Case Against Smooth Null Infinity V: Early-Time Asymptotics of Linearised Gravity Around Schwarzschild for Fixed Spherical Harmonic Modes
• Projective and Carrollian geometry at time/space-like infinity on projectively compact Ricci flat Einstein manifolds
• Asymptotics of spin-0 fields and conserved charges on n-dimensional Minkowski spaces
• Ti and Spi, Carrollian extended boundaries at timelike and spatial infinity
• Scalar subleading soft theorems from an infinite tower of charges