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Quantitative Near-Kerr Evolution and Generic C2 Future Inextendibility
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Abstract
For every fixed rotating subextremal Kerr bridge, we prove that smooth vacuum data admitting a C2 future extension of their full maximal globally hyperbolic development form a meagre set in a neighborhood defined by one finite-order seminorm. The topology allows arbitrary symbol-bounded asymptotically flat tails and imposes no symmetry.
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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)
- Maxime Van de Moortel, Mass inflation and the C^2-inextendibility of spherically symmetric charged scalar field dynamical black holes (arXiv:2001.11156, January 2020; Comm. Math. Phys.). Proves C^2 Cauchy-horizon inextendibility via mass inflation in a spherically symmetric charged model, alongside the Luk–Oh C^2 result in the paper's history section.
- 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). Linearised-gravity curvature instability of the Kerr Cauchy horizon, related to the large tidal measurement that the C^2 test violation relies on.
- Sebastian Gurriaran, Generic linearized curvature singularity at the perturbed Kerr Cauchy horizon (arXiv:2503.24114, March 2025). Generic linearized curvature blow-up at the Kerr Cauchy horizon; the bibliography cites only the author's later nonlinear paper (arXiv:2603.17911).
- Jonathan Luk, Jan Sbierski, Instability results for the wave equation in the interior of Kerr black holes (arXiv:1512.08259, December 2015). Linear-wave Cauchy-horizon instability in Kerr under event-horizon energy bounds, an earlier entry in the "Kerr interior instability" line that the history section surveys.
Digests and expositions
- Latent Seminar, Kerr cosmic censorship: curvature, holonomy, and weak connections (expository article, 2026-10-07). Explains the comparison development, finite curvature tests and Baire-category argument for C² inextendibility, 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
- Emergent Mind: family 264
Independent sites; their content is not reviewed here.
Cite
@misc{OAI:Quantitative-Near-Kerr-Evolution-and-Generic-C2-Future-Inextendibility-September-23-2026,
author = {{OpenAI}},
title = {{Quantitative Near-Kerr Evolution and Generic $C^2$ Future Inextendibility}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/Quantitative-Near-Kerr-Evolution-and-Generic-C2-Future-Inextendibility-September-23-2026/paper.pdf}{OAI:Quantitative-Near-Kerr-Evolution-and-Generic-C2-Future-Inextendibility-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 Future Inextendibility with Square-Integrable Connection Near a Fixed Kerr Spacetime · September 23, 2026
- Generic C1 Future Inextendibility Near Rotating Subextremal Kerr Spacetimes · September 23, 2026