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Generic Future Inextendibility with Square-Integrable Connection Near a Fixed Kerr Spacetime
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Abstract
For each fixed rotating subextremal Kerr background with mass M > 0 and rotation $0\lt |\mathfrak a|\lt M$, we prove that the smooth vacuum data near its complete two-ended bridge whose full maximal globally hyperbolic development admits a future $C^0\cap W^{1,2}_{\mathrm{loc}}$ extension form a meagre set in the weighted smooth topology. The extension metric is continuous and nondegenerate, and its weak connection is locally square-integrable. The neighborhood requires smallness of only the tenth weighted seminorm, while the topology tests every finite order.
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Related prior literature mentioned by others
- Mihalis Dafermos and Jonathan Luk, The interior of dynamical vacuum black holes I: The C⁰-stability of the Kerr Cauchy horizon (Annals of Mathematics 202, 309–630, 2025). The Papex overview cites continuous extendibility from suitable interior data as background to the family's stronger-regularity inextendibility claims. [family-level]
- Jonathan Luk and Sung-Jin Oh, Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data I. The interior of the black hole region (Annals of Mathematics 190, 1–111, 2019). The Papex overview cites generic C² inextendibility in the spherically symmetric Einstein–Maxwell–scalar-field model as related prior work. [family-level]
Possibly relevant literature (found by the agent, not checked)
- Jonathan Luk, Jan Sbierski, Instability results for the wave equation in the interior of Kerr black holes (arXiv:1512.08259, December 2015). Proves infinite energy at the Kerr Cauchy horizon for linear waves under event-horizon energy bounds, a linear-scalar analogue of the square-integrable threshold in the main theorem.
- Jan Sbierski, Instability of the Kerr Cauchy horizon under linearised gravitational perturbations (arXiv:2201.12295, January 2022; v2 noted as accepted in Annals of PDE). Proves a linearised-gravity Cauchy-horizon singularity for Kerr, related to the blueshifted curvature signal that the packet construction produces.
- Sebastian Gurriaran, Generic linearized curvature singularity at the perturbed Kerr Cauchy horizon (arXiv:2503.24114, March 2025). Derives spin −2 Teukolsky asymptotics giving a generic linearized curvature singularity at the Kerr Cauchy horizon; the bibliography cites only the author's later nonlinear paper (arXiv:2603.17911).
- Peter Cameron, Jan Sbierski, On the uniqueness of continuous spacetime extensions in 1+1 dimensions with applications to weak null singularities (arXiv:2511.13422, November 2025). Studies when continuous extensions across a null boundary are unique, which bears on the "equivalence with a reference continuous boundary" requirement that the introduction contrasts with its own approach.
Digests and expositions
- Latent Seminar, Kerr cosmic censorship: curvature, holonomy, and weak connections (expository article, 2026-10-07). Explains the weak-connection extension class, averaged holonomy and companion dependencies, explicitly without independently verifying the full proofs. [family-level]
- Papex, Cosmic censorship hypothesis (overview, reviewed 2026-10-14). Discusses the family's local square-integrable-connection claim alongside earlier censorship results and distinguishes the claim from independent verification. [family-level]
Elsewhere
- VibeMathed: Problem record
- Emergent Mind: family 264
Independent sites; their content is not reviewed here.
Cite
@misc{OAI:Generic-Future-Inextendibility-with-Square-Integrable-Connection-Near-a-Fixed-Kerr-Spacetime-September-23-2026,
author = {{OpenAI}},
title = {{Generic Future Inextendibility with Square-Integrable Connection Near a Fixed Kerr Spacetime}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/Generic-Future-Inextendibility-with-Square-Integrable-Connection-Near-a-Fixed-Kerr-Spacetime-September-23-2026/paper.pdf}{OAI:Generic-Future-Inextendibility-with-Square-Integrable-Connection-Near-a-Fixed-Kerr-Spacetime-September-23-2026}},
year = {2026}
}Family 264: Strong cosmic censorship near two-ended Kerr data
Proves local strong cosmic censorship near each fixed rotating subextremal Kerr bridge. A dense Gδ subset of a weighted smooth neighborhood of smooth complete two-ended asymptotically flat vacuum data has full maximal globally hyperbolic developments with no future continuous nondegenerate extension whose weak connection is locally square-integrable. No symmetry is imposed; extensions need not satisfy the vacuum equations.
Other papers in this family:
- Generic C1 Future Inextendibility Near Rotating Subextremal Kerr Spacetimes · September 23, 2026
- Quantitative Near-Kerr Evolution and Generic C2 Future Inextendibility · September 23, 2026