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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 has very sharp, discrete energy eigenstates, and the system performs very rapid transitions from one stationary state to another. For instance, when the system is in the 100th excited state, the lifetimes of the energy eigenstates are of the order of 10-30 s, and the energies of gravitons released in transitions between nearby states are of the order of 1022 eV.