Generic linearized curvature singularity at the perturbed Kerr Cauchy horizon

Fuente: arXiv
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Main Author: Gurriaran, Sebastian
Format: Preprint
Published: 2025
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_version_ 1866916667926249472
author Gurriaran, Sebastian
author_facet Gurriaran, Sebastian
contents We prove the precise asymptotics of the spin $-2$ Teukolsky field in the interior and along the Cauchy horizon of a subextremal Kerr black hole. Together with the oscillatory blow-up asymptotics of the spin $+2$ Teukolsky field proven in our previous work arXiv:2409.02670, our result suggests that generic perturbations of a Kerr black hole build up to form a coordinate-independent curvature singularity at the Cauchy horizon. This supports the Strong Cosmic Censorship conjecture in Kerr spacetimes. Unlike in the spin $+2$ case, the spin $-2$ Teukolsky field is regular on the Cauchy horizon and the first term in its asymptotic development vanishes. As a result, the derivation of a precise lower bound for the spin $-2$ field is more delicate than in the spin $+2$ case, and relies on a novel ODE method based on a decomposition of the Teukolsky operator between radial and time derivatives.
format Preprint
id arxiv_https___arxiv_org_abs_2503_24114
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Generic linearized curvature singularity at the perturbed Kerr Cauchy horizon
Gurriaran, Sebastian
General Relativity and Quantum Cosmology
Analysis of PDEs
35Q75, 58J37, 58J45, 58K55, 83C57, 83C75
We prove the precise asymptotics of the spin $-2$ Teukolsky field in the interior and along the Cauchy horizon of a subextremal Kerr black hole. Together with the oscillatory blow-up asymptotics of the spin $+2$ Teukolsky field proven in our previous work arXiv:2409.02670, our result suggests that generic perturbations of a Kerr black hole build up to form a coordinate-independent curvature singularity at the Cauchy horizon. This supports the Strong Cosmic Censorship conjecture in Kerr spacetimes. Unlike in the spin $+2$ case, the spin $-2$ Teukolsky field is regular on the Cauchy horizon and the first term in its asymptotic development vanishes. As a result, the derivation of a precise lower bound for the spin $-2$ field is more delicate than in the spin $+2$ case, and relies on a novel ODE method based on a decomposition of the Teukolsky operator between radial and time derivatives.
title Generic linearized curvature singularity at the perturbed Kerr Cauchy horizon
topic General Relativity and Quantum Cosmology
Analysis of PDEs
35Q75, 58J37, 58J45, 58K55, 83C57, 83C75
url https://arxiv.org/abs/2503.24114