  We consider the simultaneous scattering of an angular momentum carrying
Laguerre-Gaussian light beam and an acoustic wave from an atomic Bose-Einstein
condensate, under condition of optical superradiance induced vortex state. We
derive the mean field dynamical equations of the light-superfluid system, and
obtain the equations governing the elementary excitation of the system which
result in a massless Klein-Gordon equation with source terms. This equation
describes the propagation of the sound wave in an effective spacetime.
Employing a simplifying draining bathtub model for the vortex, we investigate
the scattering of the acoustic wave in the vortex phase and obtain a condition
for the acoustic superradiance. We conclude that Laguerre-Gaussian beam induced
sudden transition from homogeneous to vortex state in the superfluid
simultaneously leads to the optical and acoustic superradiance.
