The spacetime Penrose inequality: invariant ADM mass bounds the minimal area enclosing a trapped boundary, for general asymptotically flat initial data

Theorem 1.3: for smooth one-ended initial-data exteriors in every dimension $n\ge3$ with integrable constraint densities, dominant energy condition, weakly future trapped boundary ( $\theta^+\le0$ , nothing on $\theta^-$ ), the stated decay, $E>|P|$ and $A_{\min}>0$ : $m=(E^2-|P|^2)^{1/2}\ge\frac12(A_{\min}/\omega_{n-1})^{(n-2)/(n-1)}$ , sharp; outermostness and outer area minimization are not assumed. Corollary 1.4 derives $E>|P|$ ; Theorem 1.5 ( $n=3,4$ ) needs only two metric derivatives of decay. Companions: rigidity (equality only for Schwarzschild-Tangherlini slices, under horizon hypotheses), a conformal-flow Riemannian inequality in all dimensions, the boundary deformations, and a Bondi-mass version for CKS hyperboloidal data. Not shown: evolution or cosmic censorship. Priority: Allen-Bryden-Kazaras-Khuri (2025) proved the bound with a non-sharp constant.

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Occurred: Sep 27, 2026

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Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The spacetime Penrose inequality: invariant ADM mass bounds the minimal area enclosing a trapped boundary, for general asymptotically flat initial data · Spacetime Penrose inequality

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VibeMathed record: The spacetime Penrose inequality: invariant ADM mass bounds the minimal area enclosing a trapped boundary, for general asymptotically flat initial data

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No independent mathematician has checked this yet. Checked here: the abstract, introduction, Theorems 1.3 and 1.5 and Corollary 1.4 of the principal manuscript were read against the conjecture as the manuscript formulates it, and the companion abstracts were read. The proof (a coupled generalized-Jang and conformal deformation through a penalized scalar system, then a Riemannian Penrose inequality by conformal flow) was not refereed. Scope stated by the paper: smooth one-ended exteriors (designated-end versions for finitely many ends in dimensions three and four), weakly future trapped boundary, dominant energy condition, decay $g-\delta=O_6(r^{-q})$ , $K=O_5(r^{-1-q})$ with $(n-2)/2<q<n-2$ ; for $n\ge5$ positive enclosing area is assumed, while in dimensions three and four weaker decay suffices and positivity and timelikeness are conclusions. Equality is a separate companion with extra horizon hypotheses. The family's only Lean challenge (CKSBondiPenrose) covers the Cha-Khuri-Sakovich end replacement and Schwarzschild equality examples, not this inequality, so the entry is not lean-checked.

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The spacetime Penrose inequality: invariant ADM mass bounds the minimal area enclosing a trapped boundary, for general asymptotically flat initial data

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Companion: Equality and rigidity in the spacetime Penrose inequality

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