Supertranslation-Invariant Dressed Lorentz Charges

TL;DR

This paper derives explicit Lorentz charges that commute with supertranslations in asymptotically flat spacetimes, ensuring consistent algebraic structure and physical interpretation, especially in the presence of soft degrees of freedom.

Contribution

It provides a new explicit formula for Lorentz charges that commute with BMS supertranslations, using infrared regularizations and a unitary transformation.

Findings

Charges satisfy the Lorentz algebra

Consistent with supertranslated Minkowski space

Valid for boosted Kerr black holes

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.