Exterior stability of Minkowski spacetime with borderline decay

In 1993, the global stability of Minkowski spacetime was proved in the celebrated work of Christodoulou and Klainerman. In 2003, Klainerman and Nicolò revisited Minkowski stability in the exterior of an outgoing null cone. In 2023, the author extended the results of Christodoulou-Klainerman to minimal decay assumptions. In this paper, we prove that the exterior stability of Minkowski holds with decay that is borderline compared to the minimal decay considered in 2023.