Exterior stability of Minkowski spacetime with borderline decay

Abstract: In 1993, the global stability of Minkowski spacetime has been proven in the celebrated work of Christodoulou and Klainerman \cite{Ch-Kl}. In 2003, Klainerman and Nicol`o \cite{Kl-Ni} revisited Minkowski stability in the exterior of an outgoing null cone. In \cite{Shen23}, the author extended the results of \cite{Ch-Kl} to minimal decay assumptions. In this paper, we prove that the exterior stability of Minkowski holds with decay which is borderline compared to the minimal decay considered in \cite{Shen23}.