OpenAI · 260-03 · 2026-10-05 · Mathematical physics
Spacetime Penrose inequalities: enclosing area, charge, and rigidity
preprints/Spacetime-Penrose-inequalities-enclosing-area-charge-and-rigidity-October-5-2026
Family 260. Spacetime Penrose inequalities and rigidity.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Expanding universe. Language of an expanding universe or a Penrose inequality is not a de Sitter state, not Em02-E's relational lapse, and not XVI-P's QdS external-leg scheme. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. Em02-E · XVI-P
Proves the sharp enclosing-area spacetime Penrose inequality for smooth one-ended asymptotically flat initial data in every spatial dimension , under dominant energy, weak future trapping, positive enclosing area, and the stated decay assumptions. It bounds invariant ADM mass below using minimum enclosing area, with equality rigidity under additional horizon hypotheses. Charged upper-area bounds treat dyonic three-dimensional data; the higher-dimensional purely electric extension uses the matched neutral theorem.
We prove sharp spacetime Penrose inequalities for invariant ADM mass and minimum enclosing area in three and four spatial dimensions. Under their respective designated-end conventions, the neutral numerical results allow arbitrary second fundamental form, nonzero momentum, disconnected weakly future trapped boundary, and finitely many ends. Under the stated horizon hypotheses, equality for the neutral inequalities reconstructs the original exterior data as spacelike slices of Schwarzschild spacetime in three dimensions and Schwarzschild–Tangherlini spacetime in four; the four-dimensional equality theorem concerns a connected, one-ended exterior. We also prove a three-dimensional electric–magnetic charged upper-area inequality for one-ended data with nonzero momentum, with separate purely electric rest-frame corollaries allowing finitely many ends. Finally, for each fixed transverse-traceless seed and prescribed decaying solution branch, we prove a local Schwarzschild–anti-de Sitter inequality.
Preprint source and Lean scope
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A Lean scope note is stored for family 260, but it does not name this preprint. It names 260-13. This page still has the full preprint source. No compilation is asserted. O.1 stays NOT_CLOSED.
Expanding universe
Anti-de Sitter Penrose inequalities are not a de Sitter state
Family 260 records spacetime Penrose inequalities. Those preprints are anti-de Sitter or asymptotically flat. That is not a de Sitter state, not Em02-E's relational lapse, and not XVI-P's QdS external-leg scheme. The authors are OpenAI. The companion does not verify those proofs. O.1 stays NOT_CLOSED.