Discarding constrained metric components at finite radius in flat space

Determine whether, at finite radius in asymptotically flat spacetimes, one can consistently construct an operator algebra that excludes constrained components of the metric (such as the Bondi mass aspect) while retaining radiative degrees of freedom, given that the finite‑radius algebra is interacting and not free.

Background

A Page curve at null infinity can be engineered by truncating the algebra to news operators and discarding constrained quantities like the Bondi mass aspect, but this relies on the free-field nature of the strict asymptotic limit. At any finite radius, natural observables (e.g., components of the Riemann tensor and Weyl scalars) are sensitive to the mass aspect, and the operator algebra is not free, so truncations are not straightforward.

The authors emphasize that a physical observer operates at finite radius, where operator products mix metric components and thus obstruct a clean separation between radiative and constrained parts. They explicitly identify the lack of a known method to perform such a truncation at finite radius.