Precise asymptotics of the spin $+2$ Teukolsky field in the Kerr black hole interior

TL;DR

This paper rigorously characterizes the precise blow-up behavior of the spin +2 Teukolsky field inside Kerr black holes, confirming the blueshift instability and supporting the Strong Cosmic Censorship conjecture.

Contribution

It extends previous scalar wave analysis to the spin +2 Teukolsky equation, providing detailed asymptotics and a new proof of the blueshift instability in Kerr interiors.

Findings

Confirmed the oscillatory blow-up asymptotics of the Teukolsky field

Provided a new proof of the blueshift instability at the Cauchy horizon

Supported the Strong Cosmic Censorship conjecture in Kerr spacetimes

Abstract

Using a purely physical-space analysis, we prove the precise oscillatory blow-up asymptotics of the spin $+2$ Teukolsky field in the interior of a subextremal Kerr black hole. In particular, this work gives a new proof of the blueshift instability of the Kerr Cauchy horizon against linearized gravitational perturbations that was first shown by Sbierski \cite{sbierski}. In that sense, this work supports the Strong Cosmic Censorship conjecture in Kerr spacetimes. The proof is an extension to the Teukolsky equation of the work \cite{scalarMZ} by Ma and Zhang that treats the scalar wave equation in the interior of Kerr. The analysis relies on the generic polynomial decay on the event horizon of solutions of the Teukolsky equation that arise from compactly supported initial data, as recently proved by Ma and Zhang \cite{pricelaw} and Millet \cite{millet} in subextremal Kerr.