Effect of scalar potential and Karmarkar condition on charged traversable wormholes

This paper investigates charged traversable wormhole solutions in f ( R, ϕ ) modified gravity, where R denotes the Ricci scalar and ϕ represents a scalar field. Employing the Karmarkar embedding condition within a spherically symmetric spacetime, we derive exact wormhole geometries and visualize their spatial structure through three-dimensional Euclidean embeddings. Our analysis focuses on three representative f ( R, ϕ ) models, demonstrating how the synergy between modified gravity and the scalar field facilitates wormhole solutions that significantly reduce the requirement for exotic matter, as evidenced by characteristic energy condition violations. The inclusion of an electromagnetic field proves crucial for stabilizing the wormhole throat against gravitational collapse. Through a detailed examination of the equilibrium conditions, we establish stable configurations where gravitational, hydrostatic, and anisotropic forces attain precise balance according to a generalized Tolman–Oppenheimer–Volkoff equation. These findings indicate that f ( R, ϕ ) gravity provides a theoretically robust framework for traversable wormholes, potentially mitigating the need for unrealistic matter content. The resulting solutions satisfy all geometric and physical requirements for traversability while yielding testable predictions for scenarios involving modified gravity.