Phys. Rev. D, 111, L021502 (2025)

Supertranslation ambiguity in post-Minkowskian expansion

Pu-Jian Mao and Baijun Zeng

Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, 135 Yaguan Road, Tianjin 300350, China.

* pjmao@dgquanwei.com, zeng@dgquanwei.com

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.