Microscopic black-hole pairs in highly excited states

We consider the quantum mechanics of a system consisting of two identical, Planck-sized Schwarzschild black holes revolving around their common centre of mass. We find that even in a very highly excited state such a system ha s very sharp, discrete energy eigenstates, and the system performs very rap id transitions from one stationary state to another. For instance, when the system is in the 100th excited state, the lifetimes of the energy eigensta tes are of the order of 10(-30) s, and the energies of gravitons released i n transitions between nearby states are of the order of 10(22) eV.