Vector wormholes as conduits for matter interaction

TL;DR

This paper investigates how massive vector fields, which break gauge invariance, can support wormhole geometries in Einstein gravity, highlighting the role of ghost modes and matter coupling in maintaining these exotic structures.

Contribution

It demonstrates that ghost degrees of freedom in massive vector theories are essential for supporting wormholes, offering new insights into their stability and physical viability.

Findings

Ghost modes are necessary for wormhole support.

Conformal matter coupling affects energy conditions.

Massive vector fields can sustain wormhole geometries.

Abstract

In this work, we focus on the dynamics of a massive one-form field, \textbf{B}, often referred to simply as a vector field, that is minimally coupled to standard Einstein gravity. In the framework of four-dimensional spacetimes, the theory of a massive one-form propagates three massive vector degrees of freedom. The inclusion of a self-interacting potential in this theory results in the breaking of gauge invariance. The breaking of such a fundamental symmetry in Classical Electromagnetism may introduce a ghost mode in massive vector theories, which generally leads to their instability. However, in the context of wormhole physics, the existence of at least one ghost degree of freedom turns out to be a necessary condition to support these exotic geometries within effective field theories. This requirement serves as a strong motivation for our work, wherein we explore the role and phenomenology of massive one-forms, minimally coupled to Einstein gravity, in providing the necessary conditions to sustain wormhole spacetimes. We further analyze the coupling of matter fields to such a vector field through conformal couplings and explore their impact on energy conditions and the physical viability of wormhole solutions.