Existence of Static Wormhole Solutions in $f(R,G)$ Gravity

This work investigates some feasible regions for the existence of traversable wormhole geometries in $f(R,G)$ gravity, where $R$ and $G$ represent the Ricci scalar and the Gauss-Bonnet invariant respectively. Three different matter contents anisotropic fluid, isotropic fluid and barotropic fluid have been considered for the analysis. Moreover, we split $f(R,G)$ gravity model into Strobinsky like $f(R)$ model and a power law $f(G)$ model to explore wormhole geometries. We select red-shift and shape functions which are suitable for the existence of wormhole solutions for the chosen $f(R,G)$ gravity model. It has been analyzed with the graphical evolution that the null energy and weak energy conditions for the effective energy-momentum tensor are usually violated for the ordinary matter content. However, some small feasible regions for the existence of wormhole solutions have been found where the energy conditions are not violated. The overall analysis confirms the existence of the wormhole geometries in $f(R,G)$ gravity under some reasonable circumstances.