Non-existence of time-periodic solutions of the Dirac equation in a Reissner-Nordström black hole background

It is shown analytically that the Dirac equation has no normalizable, time-periodic solutions in a Reissner–Nordström black hole background; in particular, there are no static solutions of the Dirac equation in such a background metric. The physical interpretation is that Dirac particles can either disappear into the black hole or escape to infinity, but they cannot stay on a periodic orbit around the black hole.