Is the future determined?
Three AI preprints claim strong cosmic censorship, in Christodoulou’s form, near every rotating non-extremal Kerr black hole
Covers result 264 in OpenAI’s catalog: all 3 papers. See its connections to other results and the work it cites.
4:03. English captions available. The video loads from YouTube when you press play.
Chapters
The claim, in plain words
Inside a rotating black hole, the exact Kerr solution has an inner horizon, the Cauchy horizon, beyond which the initial data no longer decide what happens. Penrose’s strong cosmic censorship conjecture says this is an accident of perfect symmetry: for generic data, spacetime cannot be continued past that point. The reason is blue shift: radiation falling in late gets compressed as it piles up at the inner horizon.
The strongest form is expected to fail. In work published in 2025, Dafermos and Luk showed, for suitable data already inside the black hole, that the metric extends continuously across part of the inner horizon. Back in 2008, Christodoulou had proposed a weaker form: no extension whose connection, the derivatives of the metric, is square-integrable. A 2025 survey by Van de Moortel called that version still open.
Result 264 is three OpenAI preprints, 278 pages, dated September 23, 2026. The headline paper claims Christodoulou’s version locally, near each fixed rotating Kerr black hole that is not extremal. In a neighbourhood of the two-ended Kerr data, a dense G-delta set, generic in the sense of Baire, has developments with no continuous nondegenerate future extension whose connection is locally square-integrable. No symmetry is imposed, and the extensions need not satisfy Einstein’s equations.
What it doesn’t claim
Cosmic censorship globally, or for one-ended data that collapse from a star; Schwarzschild or extremal black holes; an open set of good data; or a positive cosmological constant. The genericity is in the sense of Baire category only.
Where it stands
- Posted as preprints
- OpenAI, three papers, 59, 68 and 151 pages, dated September 23, 2026
- Peer reviewed
- Not yet
- Checked in Lean
- No
Last checked October 19, 2026. The preprints have not been revised. There is no Lean formalization, and OSVerify has not reviewed them. We found no comment from specialists in black hole interiors. One input deserves attention. The 151-page foundation paper says it does not assume global stability of the black hole’s exterior, which is in print only for slow rotation, with full-range proofs still in preprints. Instead it proves its own control for its data class at every non-extremal rotating spin, relying on a recent unrefereed linear stability preprint by Häfner, Hintz and Vasy. That is the part most in need of expert checking.
How the proofs go
- Breaking every test. The proof is a Baire category argument: any data with an extension would pass one of countably many closed tests. Near any data that pass a test, add a tiny, very late, high-frequency packet of gravitational waves. The blue shift at the inner horizon amplifies it until the test fails.
- Three tests. The three papers use different tests: tidal curvature, holonomy around tiny loops, and holonomy averaged over many observers.
The numbers in the video
- Ours: for a black hole spinning at 0.7 of the maximum, the inner horizon’s surface gravity is 6 times the outer one’s.
- Ours: in a simple model, a field shrinks while its slope across the horizon passes 10⁷⁸. In a charged toy with assumed outgoing radiation, the mass function grows to 10¹⁴⁶.
- Ours, from the papers’ exponents: the loop test wins by 1/16 of the blue-shift rate and the averaged test by 5/32. At depth 80, in units of the blue-shift rate, the blue-shift factor is about 5 × 10³⁴.
Read the source
- Generic Future Inextendibility with Square-Integrable Connection Near a Fixed Kerr Spacetime (PDF), 59 pages.
- Generic C¹ Future Inextendibility Near Rotating Subextremal Kerr Spacetimes (PDF), 68 pages.
- Quantitative Near-Kerr Evolution and Generic C² Future Inextendibility (PDF), 151 pages.
- The collection’s catalog, where this is result 264.
The 3 papers in this result
OpenAI groups related papers, such as alternative proofs, supporting results and consequences, into one result; we label the first paper it lists the main paper and the others companions.
Transcript
Read the full script
0:00The question
Does general relativity determine the future? Inside a rotating black hole, the exact Kerr solution has an inner horizon, the Cauchy horizon, beyond which the initial data no longer decide what happens. Penrose’s strong cosmic censorship conjecture says this is an accident of perfect symmetry: for generic data, spacetime cannot be continued past that point. The reason is blue shift. Radiation falling in late gets compressed as it piles up at the inner horizon. Our computer: for a black hole spinning at 0.7 of the maximum, the inner horizon’s surface gravity is 6 times the outer one’s. In a simple model, a field’s size keeps shrinking while its slope, measured across the horizon, explodes past 10⁷⁸, and in a charged toy with assumed outgoing radiation, the mass function grows to 10¹⁴⁶. But the strongest form is expected to fail. In work published in 2025, Dafermos and Luk showed, for suitable data already inside the black hole, that the metric extends continuously across part of the inner horizon. Back in 2008, Christodoulou had proposed a weaker form: no extension whose connection, the derivatives of the metric, is square-integrable. A 2025 survey by Van de Moortel called that version still open.
1:23The claims
Result 264 is three OpenAI preprints, 278 pages, dated September 23, 2026. The headline paper claims, near each fixed rotating Kerr black hole that is not extremal, Christodoulou’s version locally: in a neighbourhood of the two-ended Kerr data, a dense G-delta set, generic in the sense of Baire, has developments with no continuous nondegenerate future extension whose connection is locally square-integrable. No symmetry is imposed, and the extensions need not satisfy Einstein’s equations. Not claimed: cosmic censorship globally, or for one-ended data that collapse from a star; Schwarzschild or extremal black holes; an open set of good data; or a positive cosmological constant. The genericity is in the sense of Baire category only. One input deserves attention. The foundation paper, 151 pages, says it does not assume global stability of the black hole’s exterior, which is in print only for slow rotation, with full-range proofs still in preprints; it proves its own control for its data class across every non-extremal rotating spin, relying on a recent unrefereed linear stability preprint by Häfner, Hintz and Vasy. That is the part most in need of expert checking.
2:45How the proofs go
The proof is a Baire category argument. Any data with an extension would pass one of countably many closed tests. Near any data that pass a test, add a tiny, very late, high-frequency packet of gravitational waves; the blue shift at the inner horizon amplifies it until the test fails. The three papers use different tests: tidal curvature, holonomy around tiny loops, and holonomy averaged over many observers. The margins are thin but positive. Our arithmetic on the papers’ exponents: the loop test wins by 1/16 of the blue-shift rate, the averaged test by 5/32. At depth 80, in units of the blue-shift rate, the blue-shift factor is about 5 × 10³⁴.
3:31Where it stands
The preprints are unrefereed and unchanged since release. There is no Lean formalization, and OSVerify has not reviewed them. We found no comment from specialists in black hole interiors. If they hold, near every rotating black hole that is not extremal, the future is generically determined: for generic nearby data, in Baire’s sense, no reasonable extension can carry spacetime past where the data stop deciding.
Spot a mistake?
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