2015/05/07 by Armando J. Cabrera Pacheco, Pengzi Miao, Pacheco, Armando J. Cabrera +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #gr-qc #math.DG
paper · pdf · doi:10.48550/arxiv.1505.01800
Theorem 1.1 significantly strengthened, the assumption on positive Ricci curvature relaxed to positive scalar curvature
openalex publication_date 2015/05/07 · arxiv created 2016/02/24 · arxiv updated 2016/02/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We obtain higher dimensional analogues of the results of Mantoulidis and Schoen in [8]. More precisely, we show that (i) any metric g with positive scalar curvature on the 3-sphere S3 can be realized as the induced metric on the outermost apparent horizon of a 4-dimensional asymptotically flat manifold with non-negative scalar curvature, whose ADM mass can be arranged to be arbitrarily close to the optimal value specified by the Riemannian Penrose inequality; (ii) any metric g with positive scalar curvature on the n-sphere Sn, with n ≥ 4 , such that (Sn, g) isometrically embeds into ℝn+1 as a star-shaped hypersurface, can be realized as the induced metric on the outermost apparent horizon of an (n+1)-dimensional asymptotically flat manifold with non-negative scalar curvature, whose ADM mass can be made to be arbitrarily close to the optimal value.