The spacetime Penrose inequality with charge and original-data rigidity

OpenAI

For the manuscript’s smooth one-ended three-dimensional Einstein–Maxwell exterior data satisfying charged dominant energy and weak future trapping assumptions, invariant ADM mass obeys m≥Q and √(A/4π)≤m+√(m²−Q²), where A is minimum enclosing area in the original metric.

Sources for this record

What was already known

A published OpenAI record concerns the neutral enclosing-area spacetime inequality. Time-symmetric charged results and other restricted settings predate this manuscript.

AI involvement AI-led

OpenAI is the credited author of this internal-model manuscript. Prior human geometric results are cited, but no claim-specific human proof check is documented.

AI institutional authorship and repository provenance support AI-led production.

Importance Major

The theorem extends the upper-area spacetime bound to charged data under the stated hypotheses.

Limitations

No completed proof check or named human explanation of the charged argument was documented. The nonextremal equality classification requires additional connected-horizon assumptions and is not included in this claim.

Technical verification Reported

The source contains a proof but no completed check of this charged theorem by a named human, proof assistant, or exact certificate is documented. Reported is the evidence default, not a finding of failure.

Human understanding Few

Default: no named human explanation of the charged comparison or rigidity mechanism is documented.

Correction and publication history

2026-10-18 · publication

If correct, the theorem extends the upper-area spacetime bound to charged data under the stated hypotheses.

Read this published revision