Traversable wormholes in non-minimal Einstein–Yang–Mills gravity: Geometry, energy conditions, and gravitational lensing

Abstract

This work presents a new class of static, spherically symmetric traversable wormhole solutions within the framework of non-minimal Einstein–Yang–Mills (EYM) gravity, where the SU(2) Yang–Mills field is purely magnetic. By adopting a constant redshift function and introducing a direct coupling between the Ricci scalar and the Yang–Mills field strength, we investigate the role of the non-minimal coupling constant $\xi$ and the magnetic charge $Q$ in shaping the wormhole geometry. Our analysis shows that for small values of $\xi$, the flare-out and throat conditions can be satisfied, allowing physically viable traversable wormholes without requiring externally introduced exotic matter. The Arnowitt–Deser–Misner (ADM) mass is evaluated, revealing that for $\xi <0.01$ it grows monotonically with charge, whereas for $\xi \gtrsim 0.01$ it decreases with increasing charge, signaling a reduction in the total mass-energy of the system. An examination of the energy conditions indicates localized violations of the null and weak energy conditions at the throat, while the strong energy condition remains satisfied. Finally, the study of gravitational lensing confirms that the deflection angle of light is consistently positive, reflecting the overall attractive nature of the wormhole’s gravitational field. These results highlight the significant role of non-minimal gauge–gravity couplings in enabling traversable wormholes with distinct observational signatures.