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

TL;DR

This paper derives precise late-time asymptotics for scalar fields inside subextreme Kerr black holes, confirming their inextendibility at the Cauchy horizon and advancing understanding of the Strong Cosmic Censorship conjecture.

Contribution

It provides a new proof of the $H^1_{loc}$-inextendibility of the Kerr Cauchy horizon under scalar perturbations, extending previous exterior asymptotics results to the interior.

Findings

Confirmed $H^1_{loc}$-inextendibility of Kerr Cauchy horizon

Derived precise late-time asymptotics for scalar fields inside Kerr black holes

Discussed analogous results in Reissner--Nordström spacetimes

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 $H^1_{\text{loc}}$-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--Nordstr\"{o}m spacetimes are also discussed.