{"id":"openai-math/The-nonmaximal-anti-de-Sitter-Penrose-Inequality-and-original-data-rigidity","pdf":"https://github.com/openai/math/blob/main/preprints/The-nonmaximal-anti-de-Sitter-Penrose-Inequality-and-original-data-rigidity-October-5-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-nonmaximal-anti-de-Sitter-Penrose-Inequality-and-original-data-rigidity-October-5-2026","tags":["general-relativity","penrose-inequality","mathematical-physics"],"score":0,"title":"The nonmaximal anti-de Sitter Penrose Inequality and original-data rigidity","domain":"Mathematical physics","family":"260","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"We prove the spacetime Penrose Inequality for smooth three-dimensional initial-data exteriors with one spherical asymptotically anti-de Sitter end, satisfying the stated decay and integrability assumptions, the dominant energy condition, and a compact weakly future outer trapped boundary. We assume that the hyperbolic metric four-flux is future timelike; its Lorentz norm is the mass, and the area is the infimum over full enclosing cuts. On the connected outermost, outer area-minimizing horizon subclass, equality characterizes the original data as a spacelike hypersurface in…","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"}