arXiv subjects

Sebastian Gurriaran

Publications and source records attributed to Sebastian Gurriaran.

4 recordsLinked to original sources

arXiv2026

Non-linear instability of the Kerr Cauchy horizon near $i_+$

We consider solutions of the Einstein vacuum equations which arise from smooth initial data on a hypersurface slightly inside a dynamical black hole settling down to a subextremal Kerr black hole, and satisfying a precise non-linear Price's law-type estimate (which we expect to hold generically). We prove that the corresponding maximal globally hyperbolic development admits a non-trivial piece of future null boundary - the Cauchy horizon - emanating from timelike infinity $i_+$, which exhibits a kind of curvature blow-up, and across which the spacetime metric is Lipschitz-inextendible. Our results thus imply a Lipschitz version of Strong Cosmic Censorship for Kerr spacetimes near timelike infinity under this Price's law-type assumption. The analysis relies on the proof of the $C^0$ stability of the Kerr Cauchy horizon by Dafermos and Luk, on the non-integrable formalism of Giorgi-Klainerman-Szeftel and principal temporal gauge of Klainerman and Szeftel used in the proof of the exterior stability of slowly rotating Kerr black holes, on the linearized analysis for the Teukolsky equation inside subextremal Kerr black holes by the author (following an earlier paper on the scalar wave equation by Ma and Zhang), and on Sbierski's criterion for Lipschitz inextendibility. More precisely, we proceed by decomposing the black hole interior into different regions equipped with appropriate gauges, allowing for a proof of stability estimates and a thorough analysis of the non-linear analog of the Teukolsky equation, from which we infer our instability results.

gr-qc↗

arXiv2025

Generic linearized curvature singularity at the perturbed Kerr Cauchy horizon

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.

gr-qc↗

arXiv2024

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

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.

gr-qc↗

arXiv2022

Surface gravity of compact non-degenerate horizons under the dominant energy condition

We prove that under the dominant energy condition any non-degenerate smooth compact totally geodesic horizon admits a smooth tangent vector field of constant non-zero surface gravity. This result generalizes previous work by Isenberg and Moncrief, and by Bustamante and Reiris to the non-vacuum case, the vacuum case being given a largely independent proof. Moreover, we prove that any such achronal non-degenerate horizon is actually a Cauchy horizon bounded on one side by a chronology violating region.

gr-qc↗