Analytical investigations on non-minimally coupled scalar fields outside neutral reflecting shells

TL;DR

This paper analytically explores the conditions under which non-minimally coupled scalar fields can exist outside neutral reflecting shells, deriving a resonance formula for allowed scalar field masses.

Contribution

It introduces a new analytical approach to determine the allowed scalar field masses in shell configurations with non-minimal coupling to the Gauss-Bonnet invariant.

Findings

Derived a compact resonance formula for scalar field masses

Identified conditions for scalar field existence outside shells

Analyzed properties of scalar fields in the small mass regime

Abstract

We study the existence of scalar fields outside neutral reflecting shells. We consider static massive scalar fields non-minimally coupled to the Gauss-Bonnet invariant. We analytically investigated properties of scalar fields through the scalar field equation. In the small scalar field mass regime, we derive a compact resonance formula for the allowed masses of scalar fields in the composed scalar field and shell configurations.