The spectroscopy of Kerr–Einstein–Maxwell-dilaton-axion: exact quasibound states, scalar cloud, horizon’s Boson statistics and superradiant

In the present study, we investigate the quasibound states, scalar cloud and superradiant of relativistic scalar fields bound to a rotating black hole in Kerr–Einstein–Maxwell-dilaton-axion theory (Kerr-EMDA). We present the exact eigensolutions of the governing Klein–Gordon equation in the black hole background. By imposing boundary conditions on the quasibound states, we are able to find the exact complex quasibound state frequencies of the corresponding radial wave functions in terms of the confluent Heun polynomial. Considering the light scalar field limit of the obtained solution, we investigate the scalar–black hole resonance configuration known as the scalar cloud. In addition, we obtain an analytical relationship between the light scalar mass and black hole spin for the scalar cloud. We explore a boson distribution function by linearly expanding the radial wave function near the black hole’s event horizon. Moreover, by applying the Damour–Ruffini method, we are able to calculate the Hawking radiation flux. In the final section, we consider a propagating wave in a slowly rotating Kerr-EMDA black hole for bosons with a much larger Compton wavelength than the size of the rotating black hole. This condition allows us to use asymptotic matching to calculate the amplification factor for scalar fields in the Kerr-EMDA black hole. We present the dependence of the amplification factor on the black hole parameters by graphical analysis.