Marginally bound resonances of charged massive scalar fields in the background of a charged reflecting shell

TL;DR

This paper analytically derives the resonance spectrum of charged massive scalar fields around a charged reflecting shell, revealing that frequencies are linked to hypergeometric function zeroes and confirming results numerically.

Contribution

The study provides a new analytical formula for the resonance frequencies of charged scalar fields in a shell background, enhancing understanding of such systems.

Findings

Resonance frequencies determined by hypergeometric function zeroes

Derived a compact analytical formula for frequencies

Numerical confirmation of the analytical spectrum

Abstract

We study {\it analytically} the characteristic resonance spectrum of charged massive scalar fields linearly coupled to a spherically symmetric charged reflecting shell. In particular, we use analytical techniques in order to solve the Klein-Gordon wave equation for the composed charged-shell-charged-massive-scalar-field system. Interestingly, it is proved that the resonant oscillation frequencies of this composed physical system are determined by the characteristic zeroes of the confluent hypergeometric function. Following this observation, we derive a remarkably compact analytical formula for the resonant oscillation frequencies which characterize the marginally-bound charged massive scalar field configurations. The analytically derived resonance spectrum is confirmed by numerical computations.