Supertranslation ambiguity in post-Minkowskian expansion

TL;DR

This paper addresses the supertranslation ambiguity in the post-Minkowskian expansion of general relativity, proposing a method to uniquely determine angular momentum loss using null infinity data, resolving a longstanding issue.

Contribution

It introduces a generic, self-contained prescription to fix supertranslation ambiguity in the PM expansion, enabling unique determination of angular momentum loss.

Findings

The method clarifies the order of angular momentum loss in gravitational scattering.

It provides a way to resolve supertranslation ambiguity using null infinity data.

The approach is applicable to post-Minkowskian expansions in general relativity.

Abstract

The supertranslation ambiguity of angular momentum is a long-standing problem in general relativity, which arises the puzzle of the angular momentum loss in the post-Minkowskian (PM) expansion. The angular momentum loss in gravitational scattering is of order $G^2$ in the linear response theory but of order $G^3$ in the amplitudes-based methods. In this paper, we propose a generic prescription to fix the supertranslation ambiguity in the PM expansion which will uniquely determine the angular momentum loss. The proposal is self-contained and involves only the null infinity data.