Traversable wormhole sourced by a generalized string fluid in the 4D Einstein-Gauss-Bonnet gravity

Abstract: We investigate traversable wormhole solutions in four-dimensional Einstein-Gauss-Bonnet (EGB) gravity coupled with a generalized string fluid background. Our analysis reveals that zero-tidal solutions meet all geometric criteria for traversability while avoiding singularities, with the Gauss-Bonnet coupling $\alpha$ modulating the throat geometry and asymptotic behavior. Varying the parameters $\alpha$ and $\varepsilon$ significantly affects curvature both near the throat and at large distances, maintaining finite values throughout spacetime. We demonstrate that the null energy condition (NEC) can be satisfied for high values of $\alpha$ ($\gtrsim 1$) and low string fluid density $\varepsilon$ ($\lesssim 0.1$), greatly reducing the exotic matter requirement compared to general relativistic wormholes. The string fluid's behavior approaches that of a cloud of strings for large $\alpha$ or $\varepsilon$. Additionally, the volume integral quantifier and complexity factor analyses show that increasing $\alpha$ reduces gravitational complexity and exotic matter content near the throat, aligning with NEC preservation. Our results establish that the combined influence of Gauss-Bonnet gravity and string-like matter can support traversable wormholes while minimizing unphysical energy conditions, offering new insights for constructing viable wormhole geometries in modified gravity.