# Non-linear Stability of the Kerr–Newman–de Sitter Family of Charged Black Holes

@article{Hintz2016NonlinearSO,
title={Non-linear Stability of the Kerr–Newman–de Sitter Family of Charged Black Holes},
author={P. Hintz},
journal={Annals of PDE},
year={2016},
volume={4},
pages={1-131}
}
• P. Hintz
• Published 2016
• Mathematics, Physics
• Annals of PDE
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 initial data of a slowly rotating Kerr–Newman–de Sitter (KNdS) black hole, then in a neighborhood of the exterior region of the black hole, the metric and the electromagnetic field decay exponentially fast to their values for a possibly different member of the… Expand
38 Citations

#### Figures from this paper

The global non-linear stability of the Kerr-de Sitter family of black holes
• Mathematics, Physics
• 2016
We establish the full global non-linear stability of the Kerr-de Sitter family of black holes, as solutions of the initial value problem for the Einstein vacuum equations with positive cosmologicalExpand
Linear stability of slowly rotating Kerr black holes
• Physics, Mathematics
• 2019
We prove the linear stability of slowly rotating Kerr black holes as solutions of the Einstein vacuum equations: linearized perturbations of a Kerr metric decay at an inverse polynomial rate to aExpand
The Linear Stability of Reissner–Nordström Spacetime for Small Charge
In this paper, we prove the linear stability to gravitational and electromagnetic perturbations of the Reissner–Nordström family of charged black holes with small charge. Solutions to the linearizedExpand
Uniqueness of Kerr–Newman–de Sitter Black Holes with Small Angular Momenta
We show that a stationary solution of the Einstein–Maxwell equations which is close to a non-degenerate Reissner–Nordström–de Sitter solution is in fact equal to a slowly rotating Kerr–Newman–deExpand
The interior of dynamical vacuum black holes I: The $C^0$-stability of the Kerr Cauchy horizon
• Physics, Mathematics
• 2017
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 dataExpand
A global analysis proof of the stability of Minkowski space and the polyhomogeneity of the metric
• Mathematics, Physics
• 2017
We first give a new proof of the non-linear stability of the $(3+1)$-dimensional Minkowski spacetime as a solution of the Einstein vacuum equation. We then show that the metric admits a fullExpand
Cosmic No-Hair in Spherically Symmetric Black Hole Spacetimes
• Physics, Mathematics
• 2018
We analyze in detail the geometry and dynamics of the cosmological region arising in spherically symmetric black hole solutions of the Einstein–Maxwell-scalar field system with a positiveExpand
Bounded Energy Waves on the Black Hole Interior of Reissner–Nordström–de Sitter
• Physics, Mathematics
• 2017
Motivated by the strong cosmic censorship conjecture, in the presence of a cosmological constant, we consider solutions of the scalar wave equation $$\Box _g\phi =0$$□gϕ=0 on fixed subextremalExpand
Asymptotic description of the formation of black holes from short-pulse data
In this thesis we present partial progress towards the dynamic formation of black holes in the four-dimensional Einstein vacuum equations from Christodoulou's short-pulse ansatz. We identify naturalExpand
The linear stability of the Schwarzschild solution to gravitational perturbations in the generalised wave gauge
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 equationsExpand

#### References

SHOWING 1-10 OF 192 REFERENCES
The global non-linear stability of the Kerr-de Sitter family of black holes
• Mathematics, Physics
• 2016
We establish the full global non-linear stability of the Kerr-de Sitter family of black holes, as solutions of the initial value problem for the Einstein vacuum equations with positive cosmologicalExpand
Linear mode stability of the Kerr-Newman black hole and its quasinormal modes.
• Physics, Medicine
• Physical review letters
• 2015
We provide strong evidence that, up to 99.999% of extremality, Kerr-Newman black holes (KNBHs) are linear mode stable within Einstein-Maxwell theory. We derive and solve, numerically, a coupledExpand
Testing the nonlinear stability of Kerr-Newman black holes
• Physics
• 2014
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,Expand
The interior of dynamical vacuum black holes I: The $C^0$-stability of the Kerr Cauchy horizon
• Physics, Mathematics
• 2017
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 dataExpand
Uniform energy bound and asymptotics for the Maxwell field on a slowly rotating Kerr black hole exterior
• Physics, Mathematics
• 2013
We consider the Maxwell equation in the exterior of a very slowly rotating Kerr black hole. For this system, we prove the boundedness of a positive definite energy on each hypersurface of constant t.Expand
The wave equation on Schwarzschild-de Sitter spacetimes
• Physics, Mathematics
• 2007
We consider solutions to the linear wave equation $\Box_g\phi=0$ on a non-extremal maximally extended Schwarzschild-de Sitter spacetime arising from arbitrary smooth initial data prescribed on anExpand
The linear stability of the Schwarzschild solution to gravitational perturbations
• Physics, Mathematics
• 2016
We prove in this paper the linear stability of the celebrated Schwarzschild family of black holes in general relativity: Solutions to the linearisation of the Einstein vacuum equations around aExpand
Quasi-normal modes for de Sitter-Reissner-Nordstr\"om Black Holes
The quasi-normal modes for black holes are the resonances for the scattering of incoming waves by black holes. Here we consider scattering of massless uncharged Dirac fields propagating in the outerExpand
Master Equations for Perturbations of Generalised Static Black Holes with Charge in Higher Dimensions
• Physics
• 2004
We extend the formulation for perturbations of maximally symmetric black holes in higher dimensions developed by the present authors in a previous paper to a charged black hole background whoseExpand
Stability of Higher-Dimensional Schwarzschild Black Holes
• Physics
• 2003
We investigate the classical stability of higher-dimensional Schwarzschild black holes with respect to linear perturbations in the framework of a gauge-invariant formalism for gravitationalExpand