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 $\href{https://mathscinet.ams.org/mathscinet/relay-station?mr=1316662}{[5]}$ in a maximal foliation. In 2003, Klainerman and Nicolò $\href{https://mathscinet.ams.org/mathscinet/relay-station?mr=1946854}{[14]}$ 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 $\href{https://mathscinet.ams.org/mathscinet/relay-station?mr=1946854}{[14]}$. Compared to $\href{https://mathscinet.ams.org/mathscinet/relay-station?mr=1946854}{[14]}$, 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 $\href{https://mathscinet.ams.org/mathscinet/relay-station?mr=1946854}{[14]}$ by the $r^p$-weighted estimates of Dafermos and Rodnianski $\href{https://mathscinet.ams.org/mathscinet/relay-station?mr=2730803}{[7]}$.

Keywords

double null foliation, geodesic foliation, Minkowski stability, peeling properties, $r^p$-weighted estimates

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Received 20 February 2023

Received revised 5 July 2023

Accepted 20 August 2023

Published 3 April 2024