Supertranslation-Invariant Dressed Lorentz Charges

TL;DR

This work provides an explicit, BMS-invariant construction of Lorentz charges that commute with l>1 supertranslations by combining infrared regularization with a unitary dressing that shifts soft data. The charges are shown to satisfy the Lorentz and Poincaré algebras, with a clear separation between hard and soft degrees of freedom via the memory operator. The framework is validated by calculations on the Minkowski vacuum, a soft-radiation–modified configuration, and a boosted Kerr solution, and it clarifies how different prescriptions relate through boundary terms and antipodal matching. Overall, the paper offers a universal, regulator-based procedure to define physically meaningful, soft-invariant observables in asymptotically flat spacetimes, with implications for gravitational memory and the infrared structure of gravity.

Abstract

We present an explicit formula for Lorentz boosts and rotations that commute with BMS supertranslations in asymptotically flat spacetimes. Key to the construction is the use of infrared regularizations and of a unitary transformation that makes observables commute with the soft degrees of freedom. We explicitly verify that our charges satisfy the Lorentz algebra and we check that they are consistent with expectations by evaluating them on the supertranslated Minkowski space and on the boosted Kerr black hole.