Impact of modified gravitational theory on the viability of wormhole structures

This paper explores the existence of viable traversable wormhole solutions in the framework of $f(R,G)$ theory, where $R$ represents the Ricci scalar and $G$ denotes the Gauss–Bonnet term. We study the wormhole geometry by focusing on a static spherical spacetime with anisotropic matter configuration. The suitable shape function for the static wormhole structure is developed through the Karmarkar condition. Using this developed shape function, we construct a wormhole geometry that fulfills all the required constraints and connects asymptotically flat regions of the spacetime. Energy bounds are examined for various $f(R,G)$ models to analyze the existence of traversable wormhole geometry. We investigate the stability of the wormhole solutions using the Tolman–Oppenheimer–Volkoff equation. The rigorous analysis and satisfaction of necessary conditions lead to the conclusion that the viable traversable wormhole solutions exist in this framework, offering a deep understanding of the spacetime and the possible existence of traversable shortcuts in the universe.