Traversable wormhole solutions in Barber's second self-creation theory

We derive traversable wormhole solutions in Barber's second self-creation theory (BSSCT) for two cases. In the first case, we use pt=npr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_{t}=np_{r}$$\end{document}, where n is an arbitrary constant to obtain the solutions of the field equations and in the second case, we consider a traceless energy-momentum tensor usually associated with the casimir effect, which implies square phi=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\square \phi =0$$\end{document} in this theory. In particular, we obtain exact solutions with the shape function b(r)=r02r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b(r)=\frac{r_{0}<^>{2}}{r}$$\end{document} in the second case. In the first case, we find that the NEC, WEC, and SEC are violated, which shows the existence of wormhole solutions in the presence of exotic matter. In the second case, we find that the wormhole solutions satisfy the null, weak, and strong energy conditions, which shows the existence of a traversable wormhole in BSSCT in the presence of non-exotic matter. In addition, we use the causality and Herrera cracking technique to study the stability of the obtained wormhole solutions and find that the solutions are unstable.