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

TL;DR

This paper demonstrates that unimodular gravity allows for exact traversable wormholes supported by standard Maxwell fields and a scalar field, bypassing the need for complex nonlinear electrodynamics.

Contribution

It introduces a novel method using unimodular gravity's dynamical cosmological term to construct wormholes supported by classical fields without nonlinear electrodynamics.

Findings

Exact scalar-Maxwell-$1(r)$ wormholes constructed

Supports wormholes with phantom scalar and linear Maxwell fields

Bypasses the need for nonlinear electrodynamics in wormhole models

Abstract

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.