  This paper presents a numerical study of the acoustic superradiance from the
single vortex state of a Bose-Einstein condensate (BEC). The draining bathtub
model of an incompressible barotropic fluid is adopted to describe the vortex.
The propagation of the velocity potential fluctuations are governed by the
massless scalar Klein-Gordon wave equation, which establishes the rotating
black-hole analogy. Hence, the amplified scattering of these fluctuations from
the vortex comprise the superradiance effect. Particular to this study, a
coordinate transformation is applied which enables the identification of the
event horizon and the ergosphere termwise in the metric. Thus, the respective
spectral solutions can be obtained asymptotically at either boundary. Further,
the time-domain calculations of the energy of the propagating perturbations and
the independently performed reflection coefficient calculations from the
asymptotic solutions of the propagating perturbations are shown to be in very
good agreement. While the former solution provides the full dynamical behavior
of the superradiance, the latter method gives the frequency spectrum of the
superradiance as a function of the rotational frequency of the vortex. Hence, a
comprehensive analysis of the superradiance effect can be conducted within this
workframe.
