Kerr Stability in External Regions

Abstract

In 2003, Klainerman and Nicolò [14] proved the stability of Minkowski in the case of the exterior of an outgoing null cone. Relying on the method used in [14], Caciotta and Nicolò [2] proved the stability of Kerr spacetime in external regions, i.e. outside an outgoing null cone far away from the Kerr event horizon. In this paper, we give a new proof of [2]. Compared to [2], 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 which contains in particular the initial data considered by Klainerman and Szeftel in [20]. Also, concerning the treatment of curvature estimates, similar to [25], we replace the vectorfield method used in [2, 14] by \(r^p\)–weighted estimates introduced by Dafermos and Rodnianski in [8].