Stability of Minkowski spacetime in exterior regions

TL;DR

This paper presents a new, simplified proof of the stability of Minkowski spacetime in exterior regions, improving previous methods by reducing derivatives needed and unifying decay treatment using $r^p$--weighted estimates.

Contribution

It introduces a novel proof that simplifies and unifies the analysis of Minkowski stability in exterior regions, replacing vectorfield methods with $r^p$--weighted estimates.

Findings

Reduced the number of derivatives required in the proof

Simplified the treatment of the last slice

Unified the decay analysis of initial data

Abstract

In 1993, the global stability of Minkowski spacetime has been proven in the celebrated work of Christodoulou and Klainerman \cite{Ch-Kl} in a maximal foliation. In 2003, Klainerman and Nic\`olo \cite{Kl-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 \cite{Kl-Ni}. Compared to \cite{Kl-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 \cite{Kl-Ni} by the $r^p$--weighted estimates of Dafermos and Rodnianski \cite{Da-Ro}.