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This paper presents a numerical study of the acoustic superradiance from thesingle vortex state of a Bose-Einstein condensate (BEC). The draining bathtubmodel of an incompressible barotropic fluid is adopted to describe the vortex.The propagation of the velocity potential fluctuations are governed by themassless scalar Klein-Gordon wave equation, which establishes the rotatingblack-hole analogy. Hence, the amplified scattering of these fluctuations fromthe vortex comprise the superradiance effect. Particular to this study, acoordinate transformation is applied which enables the identification of theevent horizon and the ergosphere termwise in the metric. Thus, the respectivespectral solutions can be obtained asymptotically at either boundary. Further,the time-domain calculations of the energy of the propagating perturbations andthe independently performed reflection coefficient calculations from theasymptotic solutions of the propagating perturbations are shown to be in verygood agreement. While the former solution provides the full dynamical behaviorof the superradiance, the latter method gives the frequency spectrum of thesuperradiance as a function of the rotational frequency of the vortex. Hence, acomprehensive analysis of the superradiance effect can be conducted within thisworkframe.

Analog Black Holes and Energy Extraction by Super-Radiance from Bose Einstein Condensates (BEC) with Constant Density