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

Abstract

This second part of the series treats spin $\pm 2$ components (or extreme components), that satisfy the Teukolsky master equation, of the linearized gravity in the exterior of a slowly rotating Kerr black hole. For each of these two components, after performing a first-order differential operator once and twice, the resulting equations together with the Teukolsky master equation itself constitute a linear spin-weighted wave system. An energy and Morawetz estimate for spin $\pm 2$ components is proved by treating this system. This is a first step in a joint work (Andersson et al. in Stability for linearized gravity on the Kerr spacetime, arXiv:1903.03859, 2019) in addressing the linear stability of slowly rotating Kerr metrics.

published version

References in corpus (3)

• Mode stability on the real axis
• Linear Stability of the Non-Extreme Kerr Black Hole
• Uniform energy bound and Morawetz estimate for extreme components of spin fields in the exterior of a slowly rotating Kerr black hole I: Maxwell field

Cited by in corpus (11)

• Stability for linearized gravity on the Kerr spacetime
• Eigenvalue repulsions and quasinormal mode spectra of Kerr-Newman: an extended study
• A Scattering Theory for Linearised Gravity on the Exterior of the Schwarzschild Black Hole I: The Teukolsky Equations
• Sharp decay estimates for massless Dirac fields on a Schwarzschild background
• Price's law for spin fields on a Schwarzschild background
• Nonlinear radiation gauge for near Kerr spacetimes
• Late-time asymptotics for geometric wave equations with inverse-square potentials
• Numerical investigation of the late-time tails of the solutions of the Fackerell-Ipser equation
• Peeling for tensorial wave equations on Schwarzschild spacetime
• Precise asymptotics of the spin $+2$ Teukolsky field in the Kerr black hole interior
• Physical-space estimates for axisymmetric waves on extremal Kerr spacetime