On the Gravitational Coupling of Klein-Gordon Particles to Matter Vorticity and Spacetime Torsion: Vorticity-Energy Correlations and Isospectrality

Abstract

We consider Klein-Gordon (KG) particles in a G & ouml;del-type universe in cosmic string spacetime within a non-minimal coupling field & Fouriertrf;(nu) = 0,& Fouriertrf;(r), 0, 0, where & Fouriertrf;(r) = eta sinh 2 mu r/2 mu. In the limit mu -> 0, the non-minimal coupling field retrieves the KG oscillators in the Som-Raychaudhuri cosmic string spacetime. This assumption provides conditional/quasi-exact solvability through confluent Heun polynomials HC alpha,beta,gamma,delta,eta,z for KG particles in G & ouml;del-type cosmic string spacetime and the non-minimal coupling field & Fouriertrf;r. Moreover, it allows exact solvability for the case eta = 0 double right arrow & Fouriertrf;(r) = 0 due to the correlation between the confluent Heun polynomials HC 0,beta,gamma, 0,eta,z and the hypergeometric polynomials 2F(1) a,b,c,z/ z - 1. In both cases (eta not equal 0 and eta = 0), we show that the radial wave functions satisfy the quantum mechanical conditions of finiteness (including r = 0 and r ->infinity) and square integrability. We also explore and report isospectralities associated with two G & ouml;del-type cosmic string spacetimes characterized by opposite matter vorticities, Omega = + Omega and Omega = -Omega, where vorticity-energy correlations are consequently reported. To the best of our knowledge, only Figueiredo et al. [9] have discussed the case eta = 0. Therefore, the methodology and results of this study have not been published elsewhere.