Linear Stability of the Non-Extreme Kerr Black Hole

Abstract

It is proven that for smooth initial data with compact support outside the event horizon, the solution of every azimuthal mode of the Teukolsky equation for general spin decays pointwise in time.

66 pages, LaTeX, 2 figures, minor improvements (published version)

References in corpus (5)

• The global non-linear stability of the Kerr-de Sitter family of black holes
• Linear Waves in the Kerr Geometry: A Mathematical Voyage to Black Hole Physics
• Local energy estimate on Kerr black hole backgrounds
• Price's Law on Nonstationary Spacetimes
• Linear Stability of Rotating Black Holes: Outline of the Proof

Cited by in corpus (14)

• Stability for linearized gravity on the Kerr spacetime
• Non-linear stability of the Kerr-Newman-de Sitter family of charged black holes
• Uniform energy bound and Morawetz estimate for extreme components of spin fields in the exterior of a slowly rotating Kerr black hole II: linearized gravity
• Mode stability on the real axis
• Linear Stability of Schwarzschild Spacetime: Decay of Metric Coefficients
• Sharp decay estimates for massless Dirac fields on a Schwarzschild background
• Price's law for spin fields on a Schwarzschild background
• Almost Price's law in Schwarzschild and decay estimates in Kerr for Maxwell field
• Numerical investigation of the late-time tails of the solutions of the Fackerell-Ipser equation
• The $\Lambda$ to zero limit of spacetimes and its physical interpretation
• Linear Stability of Rotating Black Holes: Outline of the Proof
• The decay of the $SU(2)$ Yang-Mills fields on the Schwarzschild black hole for spherically symmetric small energy initial data
• Lectures on Linear Stability of Rotating Black Holes
• Quasimodes and a lower bound for the local energy decay of the Dirac equation in Schwarzschild-Anti-de Sitter spacetime