Supertranslation ambiguity in post-Minkowskian expansion

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.