H-atom energy spectrum in open RW space time via approximated "curved" Coulomb potential

The Dirac equation with approximated “curved” Coulomb potential is studied in open Robertson Walker space-time by the NewmanPenrose formalism. Under suitable approximations on both the cosmological background and short range of the action of the potential, the confined solutions of the Dirac equation are exactly determined. By a Schrôdinger like quantization assumption they are interpreted to describe the Hydrogen atom. The corresponding discrete energy spectrum is determined.