On the linear stability of the extreme Kerr black hole under axially symmetric perturbations

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.

35 pages. 2 figures. Relevant improvement in the presentation in section 2.2

References in corpus (7)

• Gravitational instability of an extreme Kerr black hole
• Hidden symmetries and decay for the Vlasov equation on the Kerr spacetime
• Linear Waves in the Kerr Geometry: A Mathematical Voyage to Black Hole Physics
• Proof of the angular momentum-mass inequality for axisymmetric black holes
• Phase space for the Einstein equations
• Linear perturbations for the vacuum axisymmetric Einstein equations
• Instability of the extreme Kerr-Newman black-holes

Cited by in corpus (12)

• Instabilities of extremal rotating black holes in higher dimensions
• 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