∑math20

Mathematical physics · Result 264

Strong cosmic censorship near two-ended Kerr data

3 papers

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.

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▶Introduction: the problem and why it mattersin preparation
▶The presented solutionin preparation

Papers 3

First page of Generic Future Inextendibility with Square-Integrable Connection Near a Fixed Kerr Spacetime

Generic Future Inextendibility with Square-Integrable Connection Near a Fixed Kerr Spacetime

OpenAI · September 23, 2026

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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@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}
}
First page of Generic C1 Future Inextendibility Near Rotating Subextremal Kerr Spacetimes

Generic C1 Future Inextendibility Near Rotating Subextremal Kerr Spacetimes

OpenAI · September 23, 2026

For each fixed Kerr spacetime with mass M > 0 and rotation \(0\lt \mathfrak a\lt M\), we prove that a dense Gδ set of nearby smooth, complete two-ended vacuum data has a maximal globally hyperbolic development with no future C1 extension. The neighborhood and genericity are defined in a weighted smooth topology, and ambient extensions may be nonvacuum.

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Cite
@misc{OAI:Generic-C1-Future-Inextendibility-Near-Rotating-Subextremal-Kerr-Spacetimes-September-23-2026,
  author = {{OpenAI}},
  title = {{Generic $C^1$ Future Inextendibility Near Rotating Subextremal Kerr Spacetimes}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Generic-C1-Future-Inextendibility-Near-Rotating-Subextremal-Kerr-Spacetimes-September-23-2026/paper.pdf}{OAI:Generic-C1-Future-Inextendibility-Near-Rotating-Subextremal-Kerr-Spacetimes-September-23-2026}},
  year = {2026}
}
First page of Quantitative Near-Kerr Evolution and Generic C2 Future Inextendibility

Quantitative Near-Kerr Evolution and Generic C2 Future Inextendibility

OpenAI · September 23, 2026

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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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}
}

Formal verification

No Lean formalization is listed for this result yet. The repository notes that unformalized results could have issues.