Related papers: Stability for linearized gravity on the Kerr space…
In this paper, we prove energy and Morawetz estimates for solutions to the scalar wave equation in spacetimes with metrics that are perturbations, compatible with nonlinear applications, of Kerr metrics in the full subextremal range.…
After a brief introduction to the black hole stability problem, we outline our recent proof of the linear stability of the non-extreme Kerr geometry.
In a recent seminal paper \cite{D-H-R} of Dafermos, Holzegel and Rodnianski the linear stability of the Schwarzschild family of black hole solutions to the Einstein vacuum equations was established by imposing a double null gauge. In this…
In this work, we derive the global sharp decay, as both a lower and an upper bounds, for the spin $\pm \mathfrak{s}$ components, which are solutions to the Teukolsky equation, in the black hole exterior and on the event horizon of a slowly…
We prove the non-linear asymptotic stability of the Schwarzschild family as solutions to the Einstein vacuum equations in the exterior of the black hole region: general vacuum initial data, with no symmetry assumed, sufficiently close to…
We propose a new geometric framework to address the stability of the Kerr solution to gravitational perturbations in the full sub-extremal range $|a|<M$. Central to our framework is a new formulation of nonlinear gravitational perturbations…
The lack of a positive-definite and conserved energy is a serious obstacle in the black hole stability problem. In this work, we will show that there exists a positive-definite and conserved Hamiltonian energy for axially symmetric linear…
It is proven that for smooth initial data with compact support outside the event horizon, the solution of every azimuthal mode of the Teukolsky equation for general spin decays pointwise in time.
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…
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…
We uncover hidden spectral symmetries of the Teukolsky equation in Kerr(-de Sitter) black holes, recently conjectured by Aminov, Grassi and Hatsuda (arXiv: 2006.06111 and arXiv: 2007.07906, 2020) in the zero cosmological constant case.…
We prove in this paper that the Schwarzschild famiily of black holes are linearly stable as a family of solutions to the system of equations that result from expressing the Einstein vacuum equations in a generalised wave gauge. In…
We prove boundedness and polynomial decay statements for solutions of the Teukolsky system for electromagnetic-gravitational perturbations of a Kerr-Newman exterior background, with parameters satisfying $|a|, |Q| \ll M$. The identification…
Extreme black holes have been argued to be unstable, in the sense that under linearized gravitational perturbations of the extreme Kerr spacetime the Weyl scalar $\psi_4$ blows up along their event horizons at very late advanced times. We…
In this paper, we address the issue of linear stability of Schwarzschild space- time subject to certain axisymmetric perturbations. In particular, we prove that associ- ated solutions to the linearized vacuum Einstein equations centered at…
Perturbations of Kerr spacetime are typically studied with the Teukolsky formalism, in which a pair of invariant components of the perturbed Weyl tensor are expressed in terms of separable modes that satisfy ordinary differential equations.…
These notes, based on lectures given at the summer school on Asymptotic Analysis in General Relativity, collect material on the Einstein equations, the geometry of black hole spacetimes, and the analysis of fields on black hole backgrounds.…
We present a new proof of linear stability of the Schwarzschild solution to gravitational perturbations. Our approach employs the system of linearised gravity in the new geometric gauge of \cite{benomio_kerr}, specialised to the $|a|=0$…
Employing the Newman-Penrose formalism and following the classic Teukolsky-like approach, we linearise the field equations of quadratic gravity on the Kerr background and combine them with the linearised Ricci and Bianch identities. This…
In a previous work, we constructed a positive-definite total energy functional for the axially symmetric linear perturbative theory of Kerr black hole spacetimes. That work is based on the dimensional reduction of dynamical axisymmetric…