2020/10/23 by Olivier Graf, Graf, Olivier
Mathematics · Physics and Astronomy · #35B40 #35Q76 #58J45 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #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.AP #math.DG #msc:35B40 #msc:35Q76 #msc:58J45
paper · pdf · doi:10.48550/arxiv.2010.12434
246 pages, 18 figures; v2 incorporated corrections from PhD referee; submitted
openalex publication_date 2020/10/23 · arxiv created 2021/02/08 · arxiv updated 2021/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove the global nonlinear stability of Minkowski space in the context of the spacelike-characteristic Cauchy problem for Einstein vacuum equations. Spacelike-characteristic initial data are posed on a compact 3-disk and on the future complete null hypersurface emanating from its boundary. Our result extends the seminal stability result for Minkowski space proved by Christodoulou and Klainerman for which initial data are prescribed on a spacelike 3-plane. The proof relies on the classical vectorfield method and bootstrapping argument from Christodoulou-Klainerman. The main novelty is the introduction and control of new geometric constructions adapted to the spacelike-characteristic setting. In particular, it features null cones with prescribed vertices, spacelike maximal hypersurfaces with prescribed boundaries and global harmonic coordinates on Riemannian 3-disks.