61 citations · 210 across the 16 of their papers we have counts for
19 papers
Spherically symmetric inextendibility of weak null singularities with Christoffel symbols in
Peter Cameron, Jan Sbierski
Motivated by the strong cosmic censorship conjecture in general relativity, we prove the inextendibility of spherically symmetric weak null singularities as spherically symmetric L…
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 …
On the uniqueness of continuous spacetime extensions in 1+1 dimensions with applications to weak null singularities
Peter Cameron, Jan Sbierski
Motivated by weak null singularities in black hole interiors, we study 1+1 dimensional Lorentzian manifolds which admit a continuous spacetime extension across a null bound…
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…
The -inextendibility of a class of FLRW spacetimes
Jan Sbierski
This paper studies the singularity structure of FLRW spacetimes without particle horizons at the -level of the metric. We show that in the case of constant spatial curvature $…
Uniqueness and non-uniqueness results for spacetime extensions
Jan Sbierski
Given a function of a certain regularity defined on some open subset , it is a classical problem of analysis to investigate wheth…
Instability of the Kerr Cauchy horizon under linearised gravitational perturbations
Jan Sbierski
This paper establishes a mathematical proof of the blue-shift instability at the sub-extremal Kerr Cauchy horizon for the linearised vacuum Einstein equations. More precisely, we e…
On holonomy singularities in general relativity and the -inextendibility of spacetimes
Jan Sbierski
This paper investigates the structure of gravitational singularities at the level of the connection. We show in particular that for FLRW spacetimes with particle horizons a local h…
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…
Predictability of subluminal and superluminal wave equations
Felicity C. Eperon, Harvey S. Reall, Jan J. Sbierski
It is sometimes claimed that Lorentz invariant wave equations which allow superluminal propagation exhibit worse predictability than subluminal equations. To investigate this, we s…
On the proof of the -inextendibility of the Schwarzschild spacetime
Jan Sbierski
This article presents a streamlined version of the author's original proof of the -inextendibility of the maximal analytic Schwarzschild spacetime. Firstly, we deviate from th…
Timelike completeness as an obstruction to -extensions
Gregory J. Galloway, Eric Ling, Jan Sbierski
The study of low regularity (in-)extendibility of Lorentzian manifolds is motivated by the question whether a given solution to the Einstein equations can be extended (or is maxima…
Instability results for the wave equation in the interior of Kerr black holes
Jonathan Luk, Jan Sbierski
We prove that a large class of smooth solutions to the linear wave equation on subextremal rotating Kerr spacetimes which are regular and decaying along the event h…
The -inextendibility of the Schwarzschild spacetime and the spacelike diameter in Lorentzian Geometry
Jan Sbierski
The maximal analytic Schwarzschild spacetime is manifestly inextendible as a Lorentzian manifold with a twice continuously differentiable metric. In this paper, we prove the strong…
Characterisation of the Energy of Gaussian Beams on Lorentzian Manifolds - with Applications to Black Hole Spacetimes
Jan Sbierski
It is known that using the Gaussian beam approximation one can show that there exist solutions of the wave equation on a general globally hyperbolic Lorentzian manifold whose energ…
On the Existence of a Maximal Cauchy Development for the Einstein Equations - a Dezornification
Jan Sbierski
In 1969, Choquet-Bruhat and Geroch established the existence of a unique maximal globally hyperbolic Cauchy development of given initial data for the Einstein equations. Their proo…