  We calculate the decay amplitude of a harmonically trapped Bose-Einstein
condensate with attractive interaction via the Feynman path integral. We find
that when the number of particles is less than a critical number, the
condensate decays relatively slowly through quantum tunneling. When the number
exceeds the critical one, a "black hole" opens up at the center of the trap, in
which density fluctuations become large due to a negative pressure, and
collisional loss will drain the particles from the trap. As the black hole is
fed by tunneling particles, we have a novel system in which quantum tunneling
serves as a hydrodynamic source.
