Wormhole spacetimes in Palatini f(R) gravity and energy conditions

Traversable wormhole spacetimes are constructed in Palatini version of modified f(R) gravity theory. We impose that the matter supporting these spacetimes satisfies the null energy condition (NEC) and the weak energy condition (WEC). The gravitational field equations in Palatini approach are totally different to those field equations obtained in general relativity and f(R) metric approach. In this framework, by considering f(R)=R-βRn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(R)= R - \beta R^n$$\end{document} which is a given f(R) model that has consistent results with observations, the field equations have been simplified. To explicitly examine the NEC and the WEC, we take three different shape functions b(r)=r02/r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b(r)=r_0^2/r$$\end{document}, b(r)=r0r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b(r)=\sqrt{r_0r}$$\end{document}, and b(r)=r03/r2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b(r)=r_0^3/r^2$$\end{document}. Then, the existence of traversable wormholes in Palatini f(R) gravity is investigated in the absence of exotic matter. It is clearly demonstrated that the matter stress-energy tensor satisfies the NEC and the WEC.