Stability of Minkowski spacetime in exterior regions

2022/11/28 by Dawei Shen, Shen, Dawei
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Advanced Mathematical Physics Problems #Computer science #Curvature #Foliation (geology) #Geology #Geometric Analysis and Curvature Flows #Geometry #Mathematical physics #Mathematics #Minkowski space #Null (SQL) #Physics #Pure mathematics #Quantum mechanics #Space (punctuation) #Spacetime #Stability (learning theory)

paper · pdf · doi:10.48550/arxiv.2211.15230

openalex publication_date 2022/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1993, the global stability of Minkowski spacetime has been proven in the celebrated work of Christodoulou and Klainerman \citeCh-Kl in a maximal foliation. In 2003, Klainerman and Nicòlo \citeKl-Ni gave a second proof of the stability of Minkowski in the case of the exterior of an outgoing null cone. In this paper, we give a new proof of \citeKl-Ni. Compared to \citeKl-Ni, we reduce the number of derivatives needed in the proof, simplify the treatment of the last slice, and provide a unified treatment of the decay of initial data. Also, concerning the treatment of curvature estimates, we replace the vectorfield method used in \citeKl-Ni by the r^p--weighted estimates of Dafermos and Rodnianski \citeDa-Ro.

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