Normally hyperbolic trapping on asymptotically stationary spacetimes
arXiv:1811.07843 · doi:10.2140/pmp.2021.2.71
Abstract
We prove microlocal estimates at the trapped set of asymptotically Kerr spacetimes: these are spacetimes whose metrics decay inverse polynomially in time to a stationary subextremal Kerr metric. This combines two independent results. The first one is purely dynamical: we show that the stable and unstable manifolds of a decaying perturbation of a time-translation-invariant dynamical system with normally hyperbolic trapping are smooth and decay to their stationary counterparts. The second, independent, result provides microlocal estimates for operators whose null-bicharacteristic flow has a normally hyperbolic invariant manifold, under suitable non-degeneracy conditions on the stable and unstable manifolds; this includes operators on closed manifolds, as well as operators on spacetimes for which the invariant manifold lies at future infinity.
arXiv comment50 pages, 8 figures
References in corpus (16)
- The global non-linear stability of the Kerr-de Sitter family of black holes
- Uniform Decay of Local Energy and the Semi-Linear Wave Equation on Schwarzchild Space
- Decay of Solutions of the Wave Equation in the Kerr Geometry
- Analysis of linear waves near the Cauchy horizon of cosmological black holes
- A proof of Price's Law on Schwarzschild black hole manifolds for all angular momenta
- Quasi-normal modes and exponential energy decay for the Kerr-de Sitter black hole
- Asymptotic distribution of quasi-normal modes for Kerr-de Sitter black holes
- Asymptotics of linear waves and resonances with applications to black holes
- Resonance projectors and asymptotics for r-normally hyperbolic trapped sets
- Semilinear wave equations on asymptotically de Sitter, Kerr-de Sitter and Minkowski spacetimes
- Non-linear stability of the Kerr-Newman-de Sitter family of charged black holes
- Global well-posedness of quasilinear wave equations on asymptotically de Sitter spaces
- Spectral gaps for normally hyperbolic trapping
- Resonance expansions for tensor-valued waves on asymptotically Kerr-de Sitter spaces
- Global analysis of quasilinear wave equations on asymptotically Kerr-de Sitter spaces
- Non-trapping estimates near normally hyperbolic trapping