Extend the ETW singularity criterion beyond flat slicings

Determine how the proposed geometric criterion bounding the divergence of the Ricci scalar with field-space distance for ETW singularities generalizes to domain-wall flows with non-flat (AdS or dS) slicings (k≠0) and clarify its relation to existing analyses.

Background

The paper proposes a new geometric necessary condition for acceptable ETW singularities, formulated and tested for codimension-one flows with flat slicings (k=0).

The authors note that understanding its applicability to curved slicings is important for broader relevance and explicitly defer this analysis to future work.

References

Furthermore, we emphasize our analysis here is formulated for codimension-one flows with flat slicings (i.e., $k=0$ in eq:ansatzzerotemp), so determining how our results are connected to analyses with different slicings (see e.g. ) is also crucial and left for future work.

— End-of-the-World Singularities: The Good, the Bad, and the Heated-up  (2603.18133 - Calderón-Infante et al., 18 Mar 2026) in Section 6: Summary of Results and Conclusions