Quantitative Mode Stability for the Wave Equation on the Kerr Spacetime

Abstract

We give a quantitative refinement and simple proofs of mode stability type statements for the wave equation on Kerr backgrounds in the full sub-extremal range (|a| < M). As an application, we are able to quantitatively control the energy flux along the horizon and null infinity and establish integrated local energy decay for solutions to the wave equation in any bounded-frequency regime.

Final version, to appear in Annales Henri Poincare

References in corpus (5)

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Cited by in corpus (40)

• Analysis of linear waves near the Cauchy horizon of cosmological black holes
• Stability of black holes in Einstein-charged scalar field theory in a cavity
• Black hole solutions in Einstein-charged scalar field theory
• Hidden symmetries and decay for the Vlasov equation on the Kerr spacetime
• Exponentially growing finite energy solutions for the Klein-Gordon equation on sub-extremal Kerr spacetimes
• Stability for linearized gravity on the Kerr spacetime
• A scattering theory construction of dynamical vacuum black holes
• Nonlinear instability of scalar fields on extremal black holes
• Accurate mapping of spherically symmetric black holes in a parameterised framework
• A proof of Friedman's ergosphere instability for scalar waves
• 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 for the Teukolsky equation on extremal and subextremal Kerr spacetimes
• Synchronous frequencies of extremal Kerr black holes: resonances, scattering and stability
• Mode stability on the real axis
• Boundedness of massless scalar waves on Kerr interior backgrounds
• A sharp version of Price's law for wave decay on asymptotically flat spacetimes
• Asymptotics for the wave equation on differential forms on Kerr-de Sitter space
• 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
• Hidden spectral symmetries and mode stability of subextremal Kerr(-dS) black holes
• Multipole moments on the common horizon in a binary-black-hole simulation
• Near-horizon microstructure and superradiant instability of black holes
• Price's law for spin fields on a Schwarzschild background
• Positive Energy Functional for Massless Scalars in Rotating Black Hole Backgrounds of Maximal Ungauged Supergravity
• Almost Price's law in Schwarzschild and decay estimates in Kerr for Maxwell field
• Analyticity of quasinormal modes in the Kerr and Kerr-de Sitter spacetimes
• Resolvent near zero energy on Riemannian scattering (asymptotically conic) spaces
• The Teukolsky--Starobinsky constants: facts and fictions
• Boundedness and decay for the Teukolsky system of spin $\pm 2$ on Reissner-Nordström spacetime: the case $|Q|\ll M$
• Mode stability for the Teukolsky equations on Kerr-anti-de Sitter spacetimes
• Mode Stability For Massless Scalars In Five-Dimensional Black Hole Backgrounds
• Numerical investigation of the late-time tails of the solutions of the Fackerell-Ipser equation
• Mathematical Study of Scattering Resonances
• Stability study of a model for the Klein-Gordon equation in Kerr spacetime
• Exponentially-growing Mode Instability on Reissner-Nordström--Anti-de-Sitter black holes
• Physical-space estimates for axisymmetric waves on extremal Kerr spacetime
• An Approach to Stability Analyses in General Relativity via Symplectic Geometry
• Stability study of a model for the Klein-Gordon equation in Kerr space-time II
• Asymptotically Anti-de Sitter Spherically Symmetric Hairy Black Holes
• Sharp decay for Teukolsky equation in Kerr spacetimes