Extending scalar-field–time localized big bang results to other matter models

Determine whether the localized big bang stability results that use the scalar field as a time function (the approach of Beyer, Oliynyk, and Zheng for the Einstein–scalar field system) can be extended to other matter models, including the vacuum Einstein equations in spacetime dimensions ≥ 11 where quiescent behavior is expected to occur.

Background

The paper reviews localized big bang stability results that use the scalar field itself as a time function to obtain a fully hyperbolic formulation and enable spatial localization of energy estimates. While effective for the Einstein–scalar field equations, this gauge choice ties the analysis to the scalar field and raises questions about applicability to other matter contents.

The authors explicitly note that such an extension is not clear and point out its relevance in settings like the vacuum Einstein equations in higher spacetime dimensions (≥ 11), where quiescent singular behavior is expected. Their own formulation aims to avoid this limitation by employing a different time function that is independent of the matter model.

References

First, since they use the scalar field as a time coordinate, it is not clear how to extend the results to other matter models. This is relevant, for instance, in the vacuum setting with spacetime dimensions ≥ 11, where quiescent behavior is expected to occur.

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

The Belinski-Khalatnikov-Lifshitz (BKL) conjecture provides a more detailed picture about the approach to spacelike singularities.

— How much chaos can be generated by gravitational collapse before reaching the Planck scale?  (2609.11570 - Brizuela et al., 10 Sep 2026) in Section 1, Introduction