Spectral gaps for normally hyperbolic trapping

general relativity
Analyse asymptotique
asymptotic analysis
relativité générale
Grenoble
[MATH]Mathematics [math]
summer school 2014
eem2014
école d’été 2014
spectral gaps
hyperbolic trapping

Appears in collection : Summer School 2014 - Asymptotic Analysis in General Relativity

Motivated by wave decay for Kerr and Kerr‐de Sitter black holes, we study spectral gaps for codimension 2 normally hyperbolic trapped sets with smooth stable/unstable foliations. Using semiclassical defect measures, we recover the gap of Wunsch‐Zworski and Nonnenmacher‐Zworski in our case. Under the stronger assumptions of r-normal hyperbolicity and pinching, we discover further spectral gaps, meaning that resonances are stratified into bands by decay rates.