$BMS_4$ Surface-Charge Algebra via Hamiltonian Framework

TL;DR

This paper investigates the surface-charge algebra related to BMS_4 symmetry at null infinity in asymptotically flat spacetime using a Hamiltonian approach, confirming previous covariant results and identifying conditions for conserved charges.

Contribution

It provides a Hamiltonian framework analysis of BMS_4 surface charges, aligning with covariant methods and clarifying conditions for charge integrability and algebra structure.

Findings

Variation of surface charges matches covariant framework results.

Charges are integrable when the radiation field is time-independent.

Conserved charges form BMS_4 algebra without central extension.

Abstract

Surface-charge algebra associated with BMS$_4$ symmetry on the null infinity of asymptotically flat spacetime is studied via the Hamiltonian framework. A coordinate system, where boundaries of constant-time hypersurfaces cross the null infinity, is adopted. The equation itself which determines the variation of the surface charges turns out the same as that previously obtained via the covariant framework by Barnich and Troessaert, and is non-integrable for general radiation field $C_{AB}$. However, if $C_{AB}$ is independent of retarded time $u$, the variation equation is integrable and the conserved surface charges generate BMS$_4$ algebra without central extension.