Energy levels of a scalar particle in a static gravitational field close to the black hole limit

TL;DR

This paper investigates the energy levels of a scalar particle in static gravitational fields near black hole conditions, revealing the emergence of zero-energy bound states only at metric singularities.

Contribution

It provides a detailed analysis of scalar particle energy spectra in finite-sized objects approaching black hole limits, highlighting the role of metric singularities.

Findings

Zero-energy bound states occur only at metric singularities.

Energy spectrum becomes quasi-continuous near singularities.

Different interior metrics influence the existence of bound states.

Abstract

The bound-state energy levels of a scalar particle in the gravitational field of finite-sized objects with interiors described by the Florides and Schwarzschild metrics are found. For these metrics, bound states with zero energy (where the binding energy is equal to the mass of the scalar particle) only exist when a singularity occurs in the metric. For the Florides metric this singularity occurs in the black hole limit, while for the constant density (Schwarzschild interior) metric it corresponds to infinite pressure at the center. Moreover, the energy spectrum is shown to become quasi-continuous as the metric becomes singular.