Superradiant scattering of electromagnetic waves emitted from disk around Kerr black holes

We study electromagnetic perturbations around a Kerr black hole surrounded by a thin disk on the equatorial plane. Our main purpose is to reveal the black hole superradiance of electromagnetic waves emitted from the disk surface. The outgoing Kerr-Schild field is used to describe the disk emission, and the superradiant scattering is represented by a vacuum wave field which is added to satisfy the ingoing condition on the horizon. The formula to calculate the energy flux on the disk surface is presented, and the energy transport in the disk-black hole system is investigated. Within the low-frequency approximation we find that the energy extracted from the rotating black hole is mainly transported back to the disk, and the energy spectrum of electromagnetic waves observed at infinity is also discussed.