A Supertranslation-Invariant Formula for the Angular Momentum Flux in Gravitational Scattering

Abstract

The angular momentum radiated in gravitational scattering can be changed by performing a supertranslation of the asymptotic metric, i.e. by adding radiation with infinite wavelenght to the metric. This puzzling property can be avoided by adopting a supertranslation-invariant definition of the angular momentum flux in general relativity. Definitions currently available in the literature cannot reproduce the flux necessary to obtain the correct radiation reaction effects in gravitational scattering. They also disagree with computations of the flux performed using scattering amplitudes and soft graviton theorems. In this paper we provide a new supertranslation-invariant definition of the angular momentum flux in gravitational scattering that uses only asymptotic metric data and reproduces the flux necessary to obtain the correct radiation reaction effects.

9 pages. Minor misprints corrected. Closure of the rotation algebra for non-radiating spacetimes explicitly verified. To appear in Physical Review Letters

References in corpus (6)

• Radiated Angular Momentum and Dissipative Effects in Classical Scattering
• Angular momentum of zero-frequency gravitons
• Multipole Expansion of Gravitational Waves: from Harmonic to Bondi coordinates
• Angular momentum loss in gravitational scattering, radiation reaction, and the Bondi gauge ambiguity
• Supertranslation-Invariant Dressed Lorentz Charges
• Classical gravitational scattering from a gauge-invariant double copy

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• Flat from anti-de Sitter
• Angular Momentum Loss Due to Tidal Effects in the Post-Minkowskian Expansion
• Large Gauge Effects and the Structure of Amplitudes
• Angular momentum and memory effect
• ADM, BMS, and some puzzling interconnections
• On the Definition of the Spin Charge in Asymptotically-Flat Spacetimes
• Gravitational vacua in the Newman-Penrose formalism
• Supertranslation ambiguity in post-Minkowskian expansion
• On supertranslation invariant Lorentz charges
• Note on post-Minkowskian expansion and Bondi coordinates
• Lorentz Covariant Supertranslation Frames for the Angular Momentum Aspect