Superradiant instability for black holes immersed in a magnetic field

We consider the bound states of the massive scalar field around a rotating black hole immersed in the asymptotically uniform magnetic field. In the regime of slow black hole rotation, the Klein–Gordon equation allows separation of variables. We show that the growth rate of the instability can be amplified a few times by the magnetic field. The effect occurs because the magnetic field adds the “effective mass” term B|m|$B|m|$ to the scalar field potential for a Kerr black hole. In addition, and as a by-product, we discuss the behavior of the quasinormal modes for the magnetized rotating black holes.