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

TL;DR

This paper introduces a new supertranslation-invariant formula for angular momentum flux in gravitational scattering, resolving inconsistencies in previous definitions and aligning with scattering amplitude calculations.

Contribution

It proposes a novel supertranslation-invariant angular momentum flux formula based solely on asymptotic metric data, improving consistency with physical effects.

Findings

The new formula reproduces correct radiation reaction effects.

It aligns with scattering amplitude and soft graviton theorems.

Resolves ambiguities caused by supertranslations.

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.