7 papers
A note on the instability of the Kerr Cauchy horizon under linearised gravitational perturbations
Jan Sbierski
This note slightly strengthens the result of arXiv:2201.12295 on the linear instability of the Kerr Cauchy horizon. This strengthened result is used in the proof arXiv:2604.04877 o…
The formation of a weak null singularity in the interior of generic rotating black holes
Jonathan Luk, Jan Sbierski
Given a characteristic initial value problem with smooth data representing a dynamical event horizon settling down to that of Kerr in the subextremal, strictly rotating range with…
A mathematical description of the spin Hall effect of light in inhomogeneous media
Sam C. Collingbourne, Marius A. Oancea, Jan Sbierski
We study Gaussian wave packet solutions for Maxwell's equations in an isotropic, inhomogeneous medium and derive a system of ordinary differential equations that captures the leadi…
A quasilinear wave with a supersonic shock in a weak solution interrupting the classical development
Leonardo Abbrescia, Pieter Blue, Jan Sbierski +1
We study the Cauchy problem for classical and weak shock-forming solutions to a model quasilinear wave equation in dimensions arising from a convenient choice of …
Lipschitz inextendibility of weak null singularities from curvature blow-up
Jan Sbierski
We prove the -inextendibility of weak null singularities without any symmetry assumptions. The proof introduces a new strategy to infer $C^{0,1}_{\mathrm{lo…
Generic blow-up results for the wave equation in the interior of a Schwarzschild black hole
Grigorios Fournodavlos, Jan Sbierski
We study the behaviour of smooth solutions to the wave equation, , in the interior of a fixed Schwarzschild black hole. In particular, we obtain a full asymptotic exp…