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• W3100549530 startingPage "1445" @default.
• W3100549530 abstract "We describe asymptotic behavior of linear waves on Kerr(–de Sitter) black holes and more general Lorentzian manifolds, providing a quantitative analysis of the ringdown phenomenon. In particular we prove that if the initial data is localized at frequencies $${sim lambda gg 1}$$ , then the energy norm of the solution is bounded by $${mathcal{O}(lambda^{1/2} e^{-(nu_{min}-varepsilon)t/2}) + mathcal{O}(lambda^{-infty}), ,,{rm for},, t leq C log lambda, ,,{rm where},, nu_{min}}$$ is a natural dynamical quantity. The key tool is a microlocal projector splitting the solution into a component with controlled rate of exponential decay and an $${mathcal{O}(lambda e^{-(nu_{min}-varepsilon)t}) + mathcal{O}(lambda^{-infty})}$$ remainder. This splitting generalizes expansions into quasi-normal modes available in completely integrable settings. In the case of generalized Kerr(–de Sitter) black holes satisfying certain natural conditions, quasi-normal modes are localized in bands and satisfy a precise counting law." @default.
• W3100549530 created "2020-11-23" @default.
• W3100549530 creator A5026164936 @default.
• W3100549530 date "2015-01-29" @default.
• W3100549530 modified "2023-10-18" @default.
• W3100549530 title "Asymptotics of Linear Waves and Resonances with Applications to Black Holes" @default.
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• W3100549530 doi "https://doi.org/10.1007/s00220-014-2255-y" @default.
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