Dirac equation with central potential: Discrete spectrum of the hydrogen atom in the Robertson-Walker space-time

The formulation of the Dirac equation with electromagnetic field for a general space-time is specialized to the Robertson-Walker metric. For a class of physically meaningful electromagnetic potentials the angular part of the wave function separates as in the free-field case. The scheme is explicitly studied for a Coulomb potential. By using a realistic approximation method one recovers the discrete energy levels of the hydrogen atom in Minkowski space. In case of static space-time, the result is exact for zero curvature, while it is approximate for nonzero curvature. The very good order of accuracy of the result is established by a comparison with similar qualitative and perturbative results.