Spontaneous Emission of Charged Bosons from Supercritical Point Charges

We study the spontaneous emission of charged bosons from supercritical Coulomb potentials and charged black holes. We find the exact emission rate from the Bogoliubov transformation by applying the tunneling boundary condition on the Jost functions at the asymptotic boundaries. The emission rate for charged bosons in the supercritical Coulomb potential increases as the charge $Z\alpha > 1/2$ of the superatom and the energy of the bosons increase but is suppressed for large angular momenta. We discuss physical implications of the emission of charged bosons from superatoms and charged black holes.