Traversable Wormholes in non-minimal Einstein-Yang-Mills Gravity: Geometry, Energy Conditions, and Gravitational Lensing

This study presents a new class of static, spherically symmetric traversable wormhole solutions within the framework of non-minimal Einstein-Yang-Mills (EYM) gravity, where the Yang-Mills field is purely magnetic and governed by the SU(2) gauge symmetry. By incorporating a non-zero redshift function and a direct coupling between the Ricci scalar and the Yang-Mills field strength tensor, the work examines the influence of the non-minimal coupling constant $ξ$ and the magnetic charge $Q$ on the wormhole geometry. The analysis demonstrates that suitable choices of these parameters can satisfy the flare-out and throat conditions, allowing for physically viable traversable wormholes without requiring exotic matter. The study further evaluates the Arnowitt-Deser-Misner (ADM) mass, showing that quantum corrections, which are modeled through Euler-Heisenberg-type contributions, reduce the total gravitational mass and may stabilize the structure. The energy conditions are analyzed, revealing localized violations of the null and weak energy conditions at the wormhole throat, while the strong energy condition remains satisfied. Additionally, light deflection in the presence of the wormhole is calculated, indicating positive deflection angles and confirming the overall attractive nature of the gravitational field. These findings highlight the role of non-minimal gauge-gravity couplings in constructing observationally distinguishable wormhole configurations.