The scalar--Maxwell--$\Lambda(x)$ system: Wormhole spacetimes without nonlinear electrodynamics in unimodular gravity

In General Relativity, constructing exact traversable wormholes coupled to electromagnetic fields typically requires complex Non-Linear Electrodynamics (NED). We demonstrate that Unimodular Gravity (UG) elegantly resolves this limitation. By relaxing energy-momentum conservation, UG introduces a dynamical cosmological term, $\Lambda(x)$, enabling a semi-classical energy exchange between matter and the vacuum. Exploiting this mechanism, we construct exact Scalar-Maxwell-$\Lambda(x)$ wormholes. We show that, provided the shape function $b(r)$ satisfies specific geometric conditions, these exact spacetimes can be fully supported by a phantom scalar field and standard linear Maxwell electrodynamics. This approach entirely bypasses NED, highlighting UG as a powerful framework for modeling non-trivial topologies with simplified, well-understood classical fields.