Klein-Gordon particles in G\"odel-type Som-Raychaudhuri cosmic string spacetime and the phenomenon of spacetime associated degeneracies

TL;DR

This paper derives exact solutions for Klein-Gordon particles in G"odel-type cosmic string spacetimes, revealing spacetime-induced degeneracies and comparing solution methods to improve understanding of quantum effects in curved backgrounds.

Contribution

It provides comprehensive exact solutions for KG oscillators in G"odel-type spacetimes using PSLET, highlighting spacetime degeneracies and addressing limitations of previous series expansion methods.

Findings

Exact energy spectra for KG particles in G"odel-type spacetimes obtained

Demonstrated degeneracies linked to spacetime properties (STAD)

Compared solution methods, favoring PSLET over series expansions

Abstract

We argue that only exact, comprehensive, and explicit solutions for the fundamental models, the Klein-Gordon (KG) oscillators and the KG-Coulomb, would help to understand the effects of gravitational fields on the dynamics of such quantum mechanical systems. In the current methodical proposal, the effects of the gravitational fields generated by a G\"odel-type Som-Raychaudhuri (SR) cosmic string spacetime on KG-oscillators (KG-particles in general) are studied and reported. In so doing, we revisit the KG-oscillators in a topologically trivial G\"odel-type spacetime background and use textbook procedures to report its exact solution that covers even and odd parities. Next, we discuss the drawbacks associated with the power series expansion approach that implies the biconfluent Heun functions/polynomials solution. We, therefore, recollect the so called pseudo perturbative shifted L expansion technique (PSLET) as an alternative and more sophisticated method/technique. Illustrative examples are used: (i) a KG-oscillator in a topologically trivial G\"odel-type spacetime, (ii) a quasi-free KG-oscillator in G\"odel SR-type cosmic string spacetime, (iii) a KG-Coulombic particle in G\"odel SR-type cosmic string spacetime at zero vorticity, and (iv) a massless KG-particle in G\"odel SR-type cosmic string spacetime in a Cornell-type Lorentz scalar potential. The corresponding exact energies are obtained from the zeroth (leading) order correction of PSLET, where all higher order correction identically vanish. The comprehensive exactness of the reported solutions manifestly suggest degeneracies associated with spacetime (STAD) phenomenon.