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

TL;DR

This paper investigates the bound states of a scalar particle around a naked Reissner-Nordström singularity using quasiclassical methods, revealing that significant binding energies occur only when masses are near the Planck scale.

Contribution

It provides an analytical approximation for energy levels of scalar particles in this extreme gravitational setting, highlighting conditions for non-zero binding energies.

Findings

Non-vanishing binding energies require Planck-scale masses.

Derived an approximate analytical expression for energy levels.

Bound states exist only under specific mass conditions.

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.