On the linear stability of the extreme Kerr black hole under axially symmetric perturbations
arXiv:1402.2848 · doi:10.1088/0264-9381/31/19/195009
Abstract
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 particular case of Minkowski, using this energy we also prove pointwise boundedness of the perturbation in a remarkable simple way.
arXiv comment35 pages. 2 figures. Relevant improvement in the presentation in section 2.2
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- Conservation laws and flux bounds for gravitational perturbations of the Schwarzschild metric
- Geometric inequalities for black holes
- A Conserved Energy for Axially Symmetric Newman-Penrose-Maxwell Scalars on Kerr Black Holes
- On a mass functional for initial data in 4+1 dimensional spacetime
- Numerical investigation of the late-time tails of the solutions of the Fackerell-Ipser equation
- On 3+1 Lorentzian Einstein Manifolds with One Rotational Isometry
- A Positive-Definite Energy Functional for the Axisymmetric Perturbations of Kerr-Newman Black Holes
- Bounds for axially symmetric linear perturbations for the extreme Kerr black hole
- Axially Symmetric Perturbations of Kerr Black Holes I: A gauge-invariant construction of ADM Energy
- Axially Symmetric Perturbations of Kerr Black Holes II: Boundary Behaviour of the Dynamics in the Orbit Space
- Energy Extraction, or Lack Thereof