Wormhole Structures in Logarithmic-Corrected $R^2$ Gravity

This paper is devoted to find the feasible shape functions for the construction of static wormhole geometry in the frame work of logarithmic-corrected $R^2$ gravity model. We discuss the asymptotically flat wormhole solutions sustained by the matter sources with anisotropic pressure, isotropic pressure and barotropic pressure. For anisotropic case, we consider three shape functions and evaluate the null energy conditions and weak energy conditions graphically along with their regions. Moreover, for barotropic and isotropic pressures, we find shape function analytically and discuss its properties. For the formation of traversable wormhole geometries, we cautiously choose the values of parameters involved in $f(R)$ gravity model. We show explicitly that our wormhole solutions violates the non-existence theorem even with logarithmic corrections. We discuss all physical properties via graphical analysis and it is concluded that the wormhole solutions with relativistic formalism can be well justified with logarithmic corrections.