{"id":"openai-math/The-spacetime-Penrose-inequality-with-charge-and-original-data-rigidity","pdf":"https://github.com/openai/math/blob/main/preprints/The-spacetime-Penrose-inequality-with-charge-and-original-data-rigidity-October-5-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-spacetime-Penrose-inequality-with-charge-and-original-data-rigidity-October-5-2026","tags":["general-relativity","mathematical-physics","charged-initial-data"],"score":0,"title":"The spacetime Penrose inequality with charge and original-data rigidity","domain":"Mathematical physics","family":"260","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"Under the stated energy, decay, and trapping hypotheses, we prove the sharp charged spacetime Penrose upper-area inequality for one-ended three-dimensional initial data with source-free electric and magnetic fields. The theorem allows arbitrary second fundamental form, nonzero ADM momentum, and disconnected boundary. Writing m for invariant ADM mass, Q for total charge magnitude, and r A for the minimum-enclosing-area radius, the bound is m ≥ Q and $`r_A\\le m+\\sqrt{m^2-Q^2}`$. The polynomial mass bound $`m\\ge(r_A+Q^2/r_A)/2`$ is asserted only when $`r_A\\gt Q`$. When m > Q , equality under…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Spacetime Penrose inequalities: enclosing area, charge, rotation, and anti-de Sitter extensions"}