Determine whether cosmological Killing horizons produce singular asymptotic data

Determine whether the presence of cosmological Killing horizons, including cosmological horizons that coincide with Cauchy horizons of the domain of dependence of conformal infinity, manifests as divergent behavior in the asymptotic data of positive-cosmological-constant vacuum spacetimes evolved on a de Sitter background.

Background

The paper develops de Sitter spacetime as a reference background for analyzing more general spacetimes with positive cosmological constant and conformally flat conformal infinity. General asymptotic data can be evolved within the topology of the de Sitter background, even beyond the physical spacetime's domain. The unresolved issue is whether cosmological Killing horizons, often appearing as Cauchy horizons of the domain of dependence of conformal infinity, are detectable through blow-up or other divergent behavior of the asymptotic data near the limiting horizon. The authors defer this analysis to future work.

References

In particular, we aim to understand whether the presence of cosmological Killing horizons (which in many relevant spacetimes coincides with the Cauchy horizons of the domain of dependence of $I$) manifests as a divergent behavior of the asymptotic data. This analysis is left for a future publication, although we shall comment further on these ideas in Section \ref{secdiscussion}.

— Asymptotics of Killing horizons: A Characterization in de Sitter Spacetime  (2609.37427 - Peón-Nieto, 29 Sep 2026) in Section 1 (Introduction), paragraph beginning “The present paper focuses exclusively on de Sitter spacetime”

Thus, $g_{(3)}'$ diverges there, exhibiting a pathological behavior as conjectured in the previous paragraph.

— Asymptotics of Killing horizons: A Characterization in de Sitter Spacetime  (2609.37427 - Peón-Nieto, 29 Sep 2026) in Section 7 (Discussion), paragraph beginning “The situation described above arises in physically important spacetimes”

The relation between regularity at the receding cosmological horizon and the radiation condition at infinity remains to be analyzed.

— Separation of variables for coupled radiative perturbations of Kerr-Newman-de Sitter black holes  (2610.20500 - Yoshida, 14 Oct 2026) in Section 6, Summary and discussion