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Boundary graph deformations for the spacetime Penrose inequality

OpenAI · September 27, 2026

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Abstract

We construct graph and conformal deformations of trapped initial-data exteriors in three and four spatial dimensions. The resulting metrics have nonnegative scalar curvature, strictly negative inner mean curvature, a lower bound protecting every enclosing cut, and an arbitrarily small upper error in ADM energy. We also give a direct four-dimensional maximal vacuum construction that retains a noncompact decaying second fundamental form. These constructions give boundary routes to the corresponding numerical Penrose inequalities.

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Cite

@misc{OAI:Boundary-graph-deformations-for-the-spacetime-Penrose-inequality-September-27-2026,
  author = {{OpenAI}},
  title = {{Boundary graph deformations for the spacetime Penrose inequality}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Boundary-graph-deformations-for-the-spacetime-Penrose-inequality-September-27-2026/paper.pdf}{OAI:Boundary-graph-deformations-for-the-spacetime-Penrose-inequality-September-27-2026}},
  year = {2026}
}

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Family 260: Spacetime Penrose inequalities: enclosing area, charge, rotation, and anti-de Sitter extensions

Proves the sharp enclosing-area spacetime Penrose inequality for smooth one-ended asymptotically flat initial data in every spatial dimension n ≥ 3, 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.

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