相关论文: Kerr stability for small angular momentum

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…

We prove that extreme Kerr initial data set is a unique absolute minimum of the total mass in a (physically relevant) class of vacuum, maximal, asymptotically flat, axisymmetric data for Einstein equations with fixed angular momentum. These…

We prove a perturbative result concerning the uniqueness of Kerr-Newman family of black holes: given an asymptotically flat space-time with bifurcate horizons, if it agrees with a non-extremal Kerr-Newman space-time asymptotically flat at…

We prove that for axially symmetric linear gravitational perturbations of the extreme Kerr black hole there exists a positive definite and conserved energy. This provides a basic criteria for linear stability in axial symmetry. In the…

We prove global existence and decay for small-data solutions to a class of quasilinear wave equations on a wide variety of asymptotically flat spacetime backgrounds, allowing in particular for the presence of horizons, ergoregions and…

We prove stability of the family of Kasner solutions within the class of polarized $T^2$-symmetric solutions of the vacuum Einstein equations in the contracting time direction with respect to an areal time foliation. All Kasner solutions…

We prove the existence of a family of initial data for the Einstein vacuum equation which can be interpreted as the data for two Kerr-like black holes in arbitrary location and with spin in arbitrary direction. When the mass parameter of…

We provide strong evidence that, up to $99.999\%$ of extremality, Kerr-Newman black holes (KN BHs) are linear mode stable within Einstein-Maxwell theory. We derive and solve, numerically, a coupled system of two PDEs for two gauge invariant…

The linearized Kerr metric is considered and put in some Gauss coordinates which are further {\em intrinsic} ones. The linear and angular 4-momenta of this metric are calculated in these coordinates and the resulting value is just zero.…

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 $|a|=0$…

This document proves global boundedness and decay for axisymmetric perturbations of a known solution to the wave map problem from a slowly rotating $|a|\ll M$ Kerr spacetime to the hyperbolic plane. This problem is motivated by the general…

We know that Kerr black holes are stable for specific conditions.In this article, we use algebraic methods to prove the stability of the Kerr black hole against certain scalar perturbations. This provides new results for the previously…

We prove the asymptotic stability of standing kink for the nonlinear relativistic wave equations of the Ginzburg-Landau type in one space dimension: for any odd initial condition in a small neighborhood of the kink, the solution,…

A new method is proposed, that establishes a one to one correspondance between the whole set of static axially symmetric vacuum GR solutions and a specific class of stationary axially symmetric scalar-Einstein solutions having a given mass…

The current early stage in the investigation of the stability of the Kerr metric is characterized by the study of appropriate model problems. Particularly interesting is the problem of the stability of the solutions of the Klein-Gordon…

We prove the nonlinear stability of the cosmological region of Kerr de Sitter spacetimes. More precisely, we show that solutions to the Einstein vacuum equations with positive cosmological constant arising from data on a cylinder that is…

We study the dispersive properties for the wave equation in the Kerr space-time with small angular momentum. The main result of this paper is to establish Strichartz estimates for solutions of the aforementioned equation. As an application,…

In this article, we study the coupling of the Einstein field equations of general relativity to a family of models of nonlinear electromagnetic fields. The family comprises all covariant electromagnetic models that satisfy the following…

We show that, within a broad stationary-axisymmetric class, Kerr-type separability and hidden symmetry arise as a local consequence of the Einstein equations. Without assuming separability, algebraic speciality, Killing--Yano symmetry, or…

The Kerr solution is generated from the Schwarzschild solution by a simple combination of real global coordinate transformations and of invariance transformations acting on the space of stationary solutions of the Einstein-Maxwell…