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Resonances of a Schwarzschild black hole. (Les résonances d’un trou noir de Schwarzschild.) (French) Zbl 0793.53094
Summary: This paper is devoted to the theoretical and computational investigations of the scattering frequencies of scalar, electromagnetic, gravitational waves around a spherical black hole. We adopt a time dependent approach: construction of wave operators for the hyperbolic Regge-Wheeler equation; asymptotic completeness; outgoing and incoming spectral representations; meromorphic continuation of the Heisenberg matrix; approximation by dumping and cut-off of the potentials and interpretation of the semigroup \(\mathbb{Z}(t)\) in the framework of the membrane paradigm. We develop a new procedure for the computation of the resonances by the spectral analysis of the transient scattered wave, based on Prony’s algorithm.

MSC:
53Z05 Applications of differential geometry to physics
83C57 Black holes
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