On supertranslation invariant Lorentz charges

TL;DR

This paper derives expressions for supertranslation invariant Lorentz charges at spacelike and timelike infinity, demonstrating their consistency with null infinity definitions and addressing supertranslation ambiguities in gravitational charges.

Contribution

It introduces new expressions for supertranslation invariant Lorentz charges in Beig-Schmidt variables and confirms their agreement with existing null infinity definitions.

Findings

Expressions match CWY definitions at null infinity.

Addresses supertranslation ambiguities in Lorentz charges.

Extends previous work to spacelike and timelike infinity.

Abstract

In recent papers, Fuentealba, Henneaux, and Troessaert (FHT) gave definitions for supertranslation invariant Lorentz charges in the ADM Hamiltonian formalism and showed that their definitions match with the Chen, Wang, Yau (CWY) definitions of Lorentz charges at null infinity which are free from ``supertranslation ambiguities''. In this brief note, motivated by the analysis of FHT, we write expressions for the supertranslation invariant Lorentz charges in Beig-Schmidt variables at spacelike and timelike infinity. We present calculations, building upon the work of Comp\`ere, Gralla, and Wei (CGW), to show that our expressions for supertranslation invariant Lorentz charges match the CWY definitions at null infinity.