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

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 $H_{\text{loc}}^1$-inextendibility of the Kerr Cauchy horizon against scalar perturbations that is first shown by Luk–Sbierski (J. Func. Anal., 2016). The analogous results in Reissner–Nordström spacetimes are also discussed.