Traversable Wormholes induced by Stress Energy Conservation: combining Casimir Energy with a scalar field

TL;DR

This work investigates traversable wormholes sourced by a minimally coupled scalar field in combination with Casimir energy, enforcing total-energy conservation by introducing a back-reaction tensor that represents the wormhole’s gravitational response. It analyzes massless and massive scalar fields under two Casimir plate configurations (fixed separation and radially varying distance), deriving explicit shape and redshift functions and identifying the conditions under which the energy-momentum conservation is satisfied. A key finding is that most configurations require the back-reaction tensor, whereas a scalar field with potential at fixed plates can, in certain setups, avoid it; however, all solutions are confined to finite regions and are not asymptotically flat, necessitating junctions to connect to exterior spacetimes. The results illuminate the parameter dependencies (throat size, boundary locations) and demonstrate the subtle interplay between Casimir energy, scalar dynamics, and gravitational back-reaction in constructing wormhole geometries.

Abstract

We investigate possible manifolds characterizing traversable wormholes in the presence of a scalar field minimally coupled to gravity, which has both kinetic and potential energy. The feature of traversability requires the violation of the null energy condition, which, in turn, signals the existence of exotic matter with negative energy density. To achieve this, we introduce a hypothetical Casimir apparatus with plates positioned either at a parametrically fixed or radially varying distance. A consistent set of field equations requires the introduction of an auxiliary field composed solely of pressure terms, which we interpret as the gravitational back-reaction of the traversable wormhole to the original source. Interestingly, the only case that appears to avoid the need for such an auxiliary field involves a scalar field with potential energy, combined with a Casimir device with fixed plates.