We consider Klein-Gordon (KG) particles in a global monopole (GM) spacetime
within Eddington-inspired Born-Infeld gravity (EiBI-gravity) and in a Wu-Yang
magnetic monopole (WYMM). We discuss a set of KG-oscillators in such spacetime
settings. We propose a textbook power series expansion for the KG radial wave
function that allows us to retrieve the exact energy levels for KG-oscillators
in a GM spacetime and a WYMM without EiBI-gravity. We, moreover, report some
textit{conditionally exact}, closed form, energy levels (through some
parametric correlations) for KG-oscillators in a GM spacetime and a WYMM within
EiBI-gravity, and for massless KG-oscillators in a GM spacetime and a WYMM
within EiBI-gravity under the influence of a Coulomb plus linear Lorentz scalar
potential. We study and discuss the effects of the Eddington parameter
$kappa$, GM-parameter $alpha$, WYMM strength $sigma$, KG-oscillators’
frequency $Omega$, and the coupling parameters of the Coulomb plus linear
Lorentz scalar potential, on the spectroscopic structure of the KG-oscillators
at hand. Such effects are studied over a vast range of the radial quantum
number $n_rgeq 0$ and include energy levels clustering at $kappa>>1$ (i.e.,
extreme EiBI-gravity), and at $|sigma|>>1$ (i.e., extreme WYMM strength).
Examining the Conclusions and Outlining a Roadmap for Readers
In this article, the authors investigate the behavior of Klein-Gordon (KG) particles in different spacetime settings. They consider a global monopole (GM) spacetime within Eddington-inspired Born-Infeld gravity (EiBI-gravity), as well as a Wu-Yang magnetic monopole (WYMM). The focus is on studying KG-oscillators in these spacetimes and analyzing their energy levels.
To start, the authors propose a textbook power series expansion for the KG radial wave function, which allows them to obtain the exact energy levels for KG-oscillators in a GM spacetime and a WYMM without EiBI-gravity. They also report some energy levels, called “conditionally exact” and closed form, for KG-oscillators in a GM spacetime and a WYMM within EiBI-gravity. Additionally, they study the effects of various parameters on the spectroscopic structure of the KG-oscillators. These parameters include the Eddington parameter κ, GM-parameter α, WYMM strength σ, KG-oscillators’ frequency Ω, and the coupling parameters of the Coulomb plus linear Lorentz scalar potential.
The authors analyze these effects over a wide range of the radial quantum number nr ≥ 0 and investigate phenomena such as energy level clustering at extreme values of the Eddington parameter (κ ≫ 1) and extreme WYMM strength (|σ| ≫ 1).
Roadmap:
- Introduction to Klein-Gordon particles in different spacetime settings.
- Explanation of the proposed textbook power series expansion for KG radial wave function.
- Discussion on retrieving exact energy levels for KG-oscillators in a GM spacetime and a WYMM without EiBI-gravity.
- Presentation of the “conditionally exact” closed form energy levels for KG-oscillators in a GM spacetime and a WYMM within EiBI-gravity.
- Analysis of the effects of various parameters (Eddington parameter κ, GM-parameter α, WYMM strength σ, KG-oscillators’ frequency Ω, and coupling parameters of the Coulomb plus linear Lorentz scalar potential) on the spectroscopic structure of the KG-oscillators.
- Study of the spectroscopic structure over a wide range of the radial quantum number nr, including phenomena like energy level clustering at extreme values of the Eddington parameter and extreme WYMM strength.
This roadmap provides readers with a clear outline of the article’s content and helps them navigate through the different sections and topics discussed. It sets expectations for the challenges and opportunities covered, such as accurately determining energy levels, analyzing the influence of various parameters, and understanding the behavior of KG-oscillators in different spacetime settings.