General Validity of Vanishing Memory Berry Curvature

Determine whether the Berry curvature associated with gravitational memory vanishes generally, beyond the fixed BMS frame and phase convention used for the preliminary calculation.

Background

The paper introduces a Berry connection for the family of inclusive coherent radiation states and relates its curvature to the non-integrability of the phase-space displacement. Preliminary calculations indicate that the memory contribution to this curvature vanishes in one fixed BMS frame with a particular phase convention.

It remains unresolved whether this vanishing is frame- and convention-dependent or holds more generally. Establishing the answer could clarify whether memory depends on the full asymptotic state rather than only its local geometry, and could help identify supertranslation-invariant contributions to angular momentum and position shifts.

References

Interestingly, preliminary calculations suggest that the memory contribution to the Berry curvature vanishes, at least in a fixed BMS frame with a particular phase convention. If this holds more generally, then the memory may depend on the asymptotic state as a whole rather than on its local geometry.

— Inclusive Radiation and Backreaction from the Phase-Space S-Matrix  (2608.21318 - Moynihan, 21 Aug 2026) in Section 11, Discussion, p. 67