Numerical investigation of the dynamics of linear spin s fields on a Kerr background. II. Superradiant scattering

Superradiant scattering of linear spin $s=0,\pm 1,\pm 2$ fields on Kerr black hole background is investigated in the time domain by integrating numerically the homogeneous Teukolsky master equation. The applied numerical setup has already been used in studying long time evolution and tail behavior of electromagnetic and metric perturbations on rotating black hole background [arXiv:1905.09082v3]. To have a clear setup the initial data is chosen to be of the compact support, while to optimize superradiance the frequency of the initial data is fine tuned. Our most important finding is that the rate of superradiance strongly depends on the relative position of the (compact) support of the initial data and the ergoregion. When they are well-separated then only a modest -- in case of $s=0$ scalar fields negligible -- superradiance occurs, whereas it can get to be amplified significantly whenever the support of the initial data and the ergoregion overlap.