Related papers: Instability of the Kerr Cauchy horizon under linea…
In this paper we prove integrated energy and pointwise decay estimates for solutions of the vacuum linearized Einstein equation on the domain of outer communication of the Kerr black hole spacetime. The estimates are valid for the full…
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…
We present a generalization of previous results regarding the stability under gravitational perturbations of nakedly singular super extreme Kerr spacetime and Kerr black hole interior beyond the Cauchy horizon. To do so we study solutions…
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…
The evolution of weak discontinuity is investigated on horizons in the $n$-dimensional static solutions in the Einstein-Maxwell-scalar-$\Lambda$ system, including the Reissner-Nordstr\"om-(anti) de Sitter black hole. The analysis is…
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…
These lecture notes are concerned with linear stability of the non-extreme Kerr geometry under perturbations of general spin. After a brief review of the Kerr black hole and its symmetries, we describe these symmetries by Killing fields and…
We begin a program of work aimed at examining the interior of a rotating black hole with a non--zero cosmological constant. The generalisation of Teukolsky's equation for the radial mode functions is presented. It is shown that the energy…
The goal of this paper is to provide a geometric framework for analyzing the uniform decay properties of solutions to the Teukolsky equation in the fully nonlinear setting of perturbations of Kerr. It contains the first nonlinear version of…
We prove that a large class of smooth solutions $\psi$ to the linear wave equation $\Box_g\psi=0$ on subextremal rotating Kerr spacetimes which are regular and decaying along the event horizon become singular at the Cauchy horizon. More…
Using the general solution to the Einstein equations on intersecting null surfaces developed by Hayward, we investigate the non-linear instability of the Cauchy horizon inside a realistic black hole. Making a minimal assumption about the…
It has long been suggested that solutions to linear scalar wave equation $$\Box_g\phi=0$$ on a fixed subextremal Reissner-Nordstr\"om spacetime with non-vanishing charge are generically singular at the Cauchy horizon. We prove that generic…
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 of the non-linear instability of the Kerr Cauchy horizon.
The Cauchy horizon inside a perturbed Kerr black hole develops an instability that transforms it into a curvature singularity. We solve for the linearized Weyl scalars $\psi_0$ and $\psi_4$ and for the curvature scalar…
We study the linear stability problem to gravitational and electromagnetic perturbations of the extremal, $ |\mathcal{Q}|=M, $ Reissner-Nordstr\"om spacetime, as a solution to the Einstein-Maxwell equations. Our work uses and extends the…
We initiate a series of works where we study the interior of dynamical rotating vacuum black holes without symmetry. In the present paper, we take up the problem starting from appropriate Cauchy data for the Einstein vacuum equations…
Motivated by the Kerr-CFT conjecture, we investigate perturbations of the near-horizon extreme Kerr spacetime. The Teukolsky equation for a massless field of arbitrary spin is solved. Solutions fall into two classes: normal modes and…
In this work we present a formulation of the Teukolsky equation for generic spin perturbations on the hyperboloidal and horizon penetrating foliation of Kerr recently proposed by Racz and Toth. An additional, spin-dependent rescaling of the…
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 suitable upper and lower bounds, we prove that a weak null…
The extendibility of spacetime and the existence of weak solutions to the Einstein field equations beyond Cauchy horizons, is a crucial ingredient to examine the limits of General Relativity. Strong Cosmic Censorship serves as a firewall…