Low-frequency radiation from a particle falling into a Kerr black hole

In this paper we consider the low-frequency limit of the electromagnetic and gravitational radiation from a relativistic particle falling into a Kerr black hole. The radiation spectra are obtained with help of the solution of Teukolsky's equations in terms of the hypergeometric functions. It is shown that in the low-frequency limit the spectra are flat and the power radiated depends strongly on the radiation spin. Dependence of the power on the initial kinetic energy of the radiating particle has the same character as that obtained by the WKB technique for the band of frequencies, where 0=(1–u₀²/c²)^–1/2 is the particle Lorentz factor at infinity. The full energy radiated is proportional to 0 in 0 for electromagnetic radiation and to ₀³ for gravitational radiation.