Non-commutative geometries and wormhole solutions in f(G) gravity

The paper investigates the static, non-commutative solutions of wormholes (WHs) that exhibit spherical symmetry. The study is conducted in the setting of modified Gauss-Bonnet gravity. Our investigation employs two methods: to construct a shape function using a viable f(G) gravity model and to infer the f(G) model through a specific shape function. We then carefully analyze the energy constraints for both methods. Our findings reveal the following results. For each value of r, the first technique provides a physically viable solution of WH related to the ordinary matter. The second approach has a feasible solution only when the values of r are high. This study analyzes the complex procedure of the development of cosmic structures to demonstrate a connection between hypothetical and observed data.