Scalar clouds in charged stringy black hole-mirror system

It was reported that massive scalar fields can form bound states around Kerr black holes (Herdeiro and Radu, Phys. Rev. Lett. 112: 221101, 2014). These bound states are called scalar clouds; they have a real frequency omega = m Omega(H), where m is the azimuthal index and Omega(H) is the horizon angular velocity of Kerr black hole. In this paper, we study scalar clouds in a spherically symmetric background, i.e. charged stringy black holes, with the mirror-like boundary condition. These bound states satisfy the superradiant critical frequency condition omega = q Phi(H) for a charged scalar field, where q is the charge of the scalar field, and Phi(H) is the horizon's electrostatic potential. We show that, for the specific set of black hole and scalar field parameters, the clouds are only possible for specific mirror locations r(m). It is shown that analytical results of the mirror location r(m) for the clouds perfectly coincide with numerical results in the qQ << 1 regime. We also show that the scalar clouds are also possible when the mirror locations are close to the horizon. Finally, we provide an analytical calculation of the specific mirror locations r(m) for the scalar clouds in the qQ >> 1 regime.