BMS charges in polyhomogeneous spacetimes

TL;DR

This work extends the analysis of asymptotic charges to polyhomogeneous spacetimes with finite shear, showing that generalized Newman-Penrose charges are contained within the asymptotic BMS charge framework. By developing both standard and dual BMS charges up to order $ ext{O}(r^{-3})$ and mapping them to the Newman-Penrose formalism, the authors unify the non-peeling data with NP-like conserved quantities. The results demonstrate a consistent, order-by-order correspondence between BMS/dual charges and NP charges in non-smooth asymptotics, and they identify which harmonics contribute to conserved charges. This advances the understanding of gravitational charges beyond peeling spacetimes and clarifies how NP charges arise in physically realistic, polyhomogeneous settings.

Abstract

We classify the asymptotic charges of a class of polyhomogeneous asymptotically-flat spacetimes with finite shear, generalising recent results on smooth asymptotically-flat spacetimes. Polyhomogenous spacetimes are a formally consistent class of spacetimes that do not satisfy the well-known peeling property. As such, they constitute a more physical class of asymptotically-flat spacetimes compared to the smooth class. In particular, we establish that the generalised conserved non-linear Newman-Penrose charges that are known to exist for such spacetimes are a subset of asymptotic BMS charges.