OpenAI · 260-02 · 2026-10-05 · Mathematical physics
A Charged Reduction of the Spacetime Penrose Inequality in Spatial Dimensions at Least Four
preprints/A-Charged-Reduction-of-the-Spacetime-Penrose-Inequality-in-Spatial-Dimensions-at-Least-Four-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.
Using the companion neutral spacetime Penrose theorem exactly at its stated strong-decay, future-trapped, positive-area, and future-timelike scope, we prove the sharp purely electric upper-area inequality in every spatial dimension n ≥ 4 for one-ended charged data satisfying the charged dominant energy condition and , with the specified decay, integrability, and finite-flux assumptions. The data may have arbitrary interior topology and ADM momentum, with a future or past trapping sign chosen independently on each boundary component. Positive enclosing area and strict ADM timelikeness are conclusions. The polynomial mass rearrangement is asserted only when the nd power of the enclosing-area radius exceeds . When , equality under the stated connected, outermost, outer-area-minimizing future-horizon hypotheses recovers the original metric, second fundamental form, and electric field as a global spacelike slice of a Reissner–Nordström–Tangherlini exterior. The equality classification includes only slices whose induced magnetic two-form vanishes.
Preprint source and Lean scope
The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.
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.