Generic linearized curvature singularity at the perturbed Kerr Cauchy horizon
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _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 |