Subleading BMS charges and fake news near null infinity
Hadi Godazgar, Mahdi Godazgar, C. N. Pope
TL;DR
This work establishes a precise link between non-linear Newman–Penrose charges and subleading BMS charges in an asymptotically flat spacetime by expanding the Barnich–Brandt charge in 1/r. It shows that the leading r^0 BMS charge is non-integrable due to Bondi news, while a unique integrable subleading charge emerges at order r^{-3} and matches the NP charges, revealing a deep connection between asymptotic symmetries and NP integrals beyond linear order. The results clarify how fake news obstructions arise at intermediate orders and explain why only a subset of NP charges appear within this framework, with steady implications for the structure of the BMS algebra and potential gravitational-wave observables. The work sets the stage for exploring a full subleading charge algebra, extensions to rotated BMS symmetries, and applications to waveforms near null infinity.
Abstract
In this paper we establish a relation between the non-linearly conserved Newman-Penrose charges and certain subleading terms in a large-$r$ expansion of the BMS charges in an asymptotically-flat spacetime. We define the subleading BMS charges by considering a $1/r$-expansion of the Barnich-Brandt prescription for defining asymptotic charges in an asymptotically-flat spacetime. At the leading order, i.e. $1/r^0$, one obtains the standard BMS charges, which would be integrable and conserved in the absence of a flux term at null infinity, corresponding to gravitational radiation, or Bondi news. At subleading orders, analogous terms in general provide obstructions to the integrability of the corresponding charges. Since the subleading terms are defined close to null infinity, but vanish actually at infinity, the analogous obstructions are not associated with genuine Bondi news. One may instead describe them as corresponding to "fake news." At order $r^{-3}$, we find that a set of integrable charges can be defined and that these are related to the ten non-linearly conserved Newman-Penrose charges.