Validation of Energy Conditions in Wormhole Geometry within Viable $f(R)$ Gravity

Abstract: In this work, wormholes, tunnel like structures introduced by Morris & Thorne \cite{Morris95}, are explored within the framework of $f(R)$ gravity. Using the shape function $b(r)=r_0\big(\frac{r}{r_0}\big)^\gamma$, where $0<\gamma<1$, and the equation of state $p_r=\omega\rho$, the $f(R)$ function is derived and the field equations are solved. Then null, weak, strong and dominated energy conditions are analyzed and spherical regions satisfying these energy conditions are determined. Furthermore, we calculated the range of the radius of the throat of the wormhole, where the energy conditions are satisfied.