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

Abstract

In General Relativity, supporting known traversable wormhole geometries with 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 show how established exact wormhole spacetimes can be fully supported by a phantom scalar field coupled to standard linear Maxwell electrodynamics. We demonstrate that, provided the shape function $b(r)$ satisfies specific geometric conditions, this non-conservative framework naturally accommodates these solutions. By providing a new physical matter source mechanism that entirely bypasses the need for NED, our main contribution highlights UG as a powerful framework for sustaining established non-trivial topologies with simplified, well-understood classical fields.

version published in CQG