Scattering and absorption of a scalar field impinging on a charged black
  hole in the Einstein-Maxwell-dilaton theory
  This study revisits the absorption and scattering process by which a massless
scalar field impinges on a charged dilatonic black hole. First, we review the
classical analysis to obtain the deflection angle and the differential
scattering cross-section. Then, using the partial wave method, we determine the
total absorption cross-section numerically in terms of the decoupling parameter
called $M\omega$, finding that the amplitude of the dilatonic black hole is
lower than the Reissner-Nordstr\"om one for mild frequencies. In the
high-frequency limit, the absorption cross-section exhibits two different
complex behaviors; the fine structure and the hyperfine structure. For the
differential scattering cross-section, smaller values of $M\omega$ lead to more
significant amplitudes; the opposite scenario is obtained by increasing the
charge-to-mass ratio. To fully grasp the main properties of the charged
dilatonic black hole, we consider a different framework where the compact
object is impinged by a charged massive scalar field. The superradiant effect
is lessened for intermediate frequency concerning the Reissner-Nordstr\"om
case. However, this effect does not necessarily imply the existence of any
dynamical instability. In order to trigger the superradiant instability,
unstable modes must remain trapped outside the event horizon with a mechanism
based on the reflecting-mirror boundary conditions. In this way, a charged
scalar field plus a charged black hole configure a charged black hole bomb. We
provide an analytic formula (lower bound) for the values of the charge field,
which can trigger this superradiant instability. We extend this minimal setup
by considering the dilaton perturbations while freezing the other degree of
freedom. The new perturbation scheme enhances the superradiance scattering and
reduces the lower bound of the charge-to-mass ratio to develop a superradiant
instability.
