Quasinormal modes for the Kerr black hole
arXiv:2407.04612
Abstract
We provide a rigorous definition of quasinormal modes for the Kerr black hole. They are obtained as the discrete set of poles of the meromorphically continued cutoff resolvent. The construction combines the method of complex scaling near asymptotically flat infinity with microlocal methods near the black hole horizon. We study the distribution of quasinormal modes in both the high and low energy regimes. We establish the existence of a high energy spectral gap and exclude the accumulation of quasinormal modes at zero energy.
79 pages, 5 figures. Added Figure 1 illustrating resonance free regions, additional details in the proof of Theorem 1.1, fixed minor error in Proposition 5.8