Precise late-time asymptotics of scalar field in the interior of a subextreme Kerr black hole and its application in Strong Cosmic Censorship conjecture

Abstract

In this work, we compute the precise late-time asymptotics for the scalar field in the interior of a non-static subextreme Kerr black hole, based on recent progress on deriving its precise asymptotics in the Kerr exterior region. This provides a new proof of the generic H loc 1 H^1_{\text {loc}} -inextendibility of the Kerr Cauchy horizon against scalar perturbations that was first shown by Luk–Sbierski [J. Funct. Anal. 271 (2016), pp. 1948–1995]. The analogous results in Reissner–Nordström spacetimes are also discussed.