相关论文: Kerr stability for small angular momentum

We show that a stationary solution of the Einstein-Maxwell equations which is close to a non-degenerate Reissner-Nordstr\"om-de Sitter solution is in fact equal to a slowly rotating Kerr-Newman-de Sitter solution. The proof uses the…

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…

The reduced (in the angular coordinate $\phi$) wave equation and Klein-Gordon equation are considered on a Kerr background and in the framework of $C^{0}$-semigroup theory. Each equation is shown to have a well-posed initial value…

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…

In this paper, we prove energy and Morawetz estimates for solutions to Teukolsky equations in spacetimes with metrics that are perturbations, compatible with nonlinear applications, of Kerr metrics in the full subextremal range. The…

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 paper, we prove a series of results concerning the uniqueness of Kerr-de Sitter as a family of smooth stationary black hole solutions to the nonlinear Einstein vacuum equations with positive cosmological constant $\Lambda$. The…

We construct a one-parameter family of stationary axisymmetric and asymptotically flat spacetimes solutions to the Einstein-Vlasov system bifurcating from the Kerr spacetime. The constructed solutions have the property that the spatial…

We prove the global non-linear stability, without symmetry assumptions, of slowly rotating charged black holes in de Sitter spacetimes in the context of the initial value problem for the Einstein-Maxwell equations: If one perturbs the…

The resolution of the nonlinear stability of black holes as solutions to the Einstein equations relies crucially on imposing the right geometric gauge conditions. In the vacuum case, the use of Generally Covariant Modulated (GCM) spheres…

We give a quantitative refinement and simple proofs of mode stability type statements for the wave equation on Kerr backgrounds in the full sub-extremal range (|a| < M). As an application, we are able to quantitatively control the energy…

It is shown that the Kerr solution exists in the generalized hybrid metric-Palatini gravity theory and that for certain choices of the function $f(R,\mathcal R)$ that characterizes the theory, the Kerr solution can be stable against…

We consider (2+1)-dimensional beams, whose transverse size may be comparable to or smaller than the carrier wavelength, on the basis of an extended version of the nonlinear Schr\"{o}dinger equation derived from the Maxwell`s equations. As…

In this paper, we prove the linear stability of weakly charged and slowly rotating Kerr-Newman black holes under coupled gravitational and electromagnetic perturbations. We show that the solutions to the linearized Einstein-Maxwell…

We prove the existence of a family of initial data for Einstein equations which represent small deformations of the extreme Kerr black hole initial data. The data in this family have the same asymptotic geometry as extreme Kerr. In…

We describe conditions assuring that the Kerr--Schild type solutions of Einstein equations with pure radiation fields are asymptotically flat at future null infinity. Such metrics cannot describe ``true'' gravitational radiation from…

This paper concludes the series begun in [M. Dafermos and I. Rodnianski, Decay for solutions of the wave equation on Kerr exterior spacetimes I-II: the cases |a| << M or axisymmetry, arXiv:1010.5132], providing the complete proof of…

The nonlinear stability of Kerr-Newman black holes (KNBHs) is investigated by performing numerical simulations within the full Einstein-Maxwell theory. We take as initial data a KNBH with mass $M$, angular momentum to mass ratio $a$ and…

We consider a class of fully nonlinear Schr\"odinger equations and we prove the existence and the stability of Cantor families of quasi-periodic, small amplitude solutions. We deal with reversible autonomous nonlinearities and we look for…

We show a stability result for the Schwarzschild singularity (inside the black hole region) for the Einstein vacuum equations. The result is proven in the class of polarized axial symmetry, under perturbations of the Schwarzschild data…