Stability of Minkowski spacetime in exterior regions

In 1993, the global stability of Minkowski spacetime has been proven in the celebrated work of Christodoulou and Klainerman [5] in a maximal foliation. In 2003, Klainerman and Nicolo [14] 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 [14]. Compared to [14], 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 [14] by the rp-weighted estimates of Dafermos and Rodnianski [7].