Klein-Gordon Particles in Cosmic String Spacetime: The Noninertial Effects of a Two-Way Rotating Frame and the Associated Degeneracies

Abstract

We investigate and discuss Klein-Gordon (KG) particles in cosmic string spacetime under the noninertial effects of a two-way rotating frame. In doing so, we report on the related gravitational effects on the energy levels of KG oscillators, KG-Coulombic particles, and KG-Coulombic particles under the influence of a Lorentz scalar shifted-linear potential S(r)=ar+b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S(r)=ar+b$$\end{document}. In addition to being new models, in a two-way rotating frame, they are observed to admit two-way rotation-associated degeneracies, such that Enr,m-Omega+=Enr,m+Omega-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_{n_{r},m_{-}}{\Omega _{+}}=E_{n_{r},m_{+}}{\Omega _{-}}$$\end{document} and Enr,m+Omega+=Enr,m-Omega-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_{n_{r},m_{+}}{\Omega _{+}}=E_{n_{r},m_{-}}{\Omega _{-}}$$\end{document}, where Omega=Omega +/-=+/-|Omega|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega =\Omega _\pm =\pm |\Omega |$$\end{document} identifies positive and negative angular velocities, m=m +/-=+/-|m|=0,+/- 1,+/- 2,& mldr;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m=m_\pm =\pm |m|=0,\pm 1,\pm 2,\ldots $$\end{document} identifies the magnetic quantum number, and nr=0,1,2,& mldr;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n_r=0,1,2,\ldots $$\end{document} identifies the radial quantum number. The effect of a two-way rotating frame in cosmic string spacetime is observed only in the energies of the KG particles in the form of -m Omega\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-m\Omega $$\end{document}, which clearly suggests the associated degeneracies mentioned above. To the best of our knowledge, such results and observations have not been reported elsewhere.