Whether localized solutions induce geometric initial data on the singularity

Ascertain whether the localized Einstein–scalar field solutions constructed by Beyer, Oliynyk, and Zheng induce geometric initial data on the big bang singularity in the sense of Ringström or of Franco‑Grisales and Ringström.

Background

The authors compare earlier localized stability results with recent asymptotic frameworks that characterize quiescent big bang singularities via geometric initial data on the singularity. They observe an incompatibility between the conclusions of the earlier localized results and the newer asymptotic results, leading to uncertainty about whether the earlier solutions admit geometric data on the singularity.

Their new formulation is designed to be compatible with the geometric initial data framework, but they explicitly flag that for the prior localized results, this issue remains unresolved.

References

And second, their conclusions are incompatible with the recent asymptotic results of [franco_complete_asymptotics_2026], so it is unclear whether their solutions induce geometric initial data on the singularity as in [ringstrom_initial_2025] or [franco-grisales_developments_2025]; see [Remark~1.4][zheng_localized_2026].

— Localized formation of quiescent big bang singularities  (2604.02104 - Franco-Grisales, 2 Apr 2026) in Introduction (discussion of prior localized results and their compatibility with asymptotic frameworks)