Naked Reissner-Nordstr\"om singularity and quasiclassical bound states

Abstract

The bound-state problem for an uncharged massive scalar particle in the field of a naked Reissner-Nordstr\"om singularity is approached by means of the quasiclassical Bohr-Sommerfeld quantization. An approximate analytical expression for the energy levels of the system is derived. It is shown that in order to obtain non-vanishing binding energies the masses of both the central object and the particle should be comparable with the Planck mass.