  We theoretically investigate the spontaneous quantum emission of phonon pairs
by superradiant processes in an atomic Bose-Einstein condensate subject to a
synthetic vector potential. Within the analog gravity perspective, this effect
corresponds to the spontaneous emission of radiation from the ergosurface of
rotating black holes. A general input-output formalism is built and used to
characterize the spectral and correlation properties of the emission.
Experimentally accessible signatures of the emission are pointed out in the
correlation functions of the atomic gas.
