Tower of subleading dual BMS charges

TL;DR

The authors construct a comprehensive tower of dual gravitational BMS charges by introducing a covariant 2-form $ ilde{H}$, extending dual charges to the full BMS group and to subleading $1/r$ orders away from null infinity. At leading order, the dual charges reproduce the real/imaginary decomposition of a complex NP-like charge, and at higher orders, they generate subleading dual charges whose integrable parts align with the NP charges, including the previously missing imaginary components. The framework mirrors the Barnich–Brandt charges but provides a magnetic/dual interpretation that does not rely on the Einstein equations, and it yields a charge algebra BB with well-defined boundary behavior. Collectively, the leading and subleading dual charges account for all ten non-linear NP charges, thus offering a unified dual description of asymptotic gravitational charges in asymptotically flat spacetimes.

Abstract

We supplement the recently found dual gravitational charges with dual charges for the whole BMS symmetry algebra. Furthermore, we extend the dual charges away from null infinity, defining subleading dual charges. These subleading dual charges complement the subleading BMS charges in the literature and together account for all the Newman-Penrose charges.