Noncommutative-geometry wormholes based on the Casimir effect

TL;DR

This paper explores how noncommutative geometry combined with the Casimir effect can theoretically support macroscopic wormholes by modifying the energy-momentum tensor without altering Einstein's equations.

Contribution

It introduces a novel approach linking noncommutative geometry and the Casimir effect to sustain large-scale wormholes without requiring exotic matter.

Findings

Noncommutative effects modify the energy-momentum tensor.

Macroscopic wormholes are theoretically supported.

Small-scale quantum effects can influence large-scale spacetime structures.

Abstract

While wormholes are as good a prediction of Einstein's theory as black holes, they are subject to severe restrictions from quantum field theory. In particular, holding a wormhole open requires a violation of the null energy condition, calling for the existence of exotic matter. The Casimir effect has shown that this physical requirement can be met on a small scale, thereby solving a key conceptual problem. The Casimir effect does not, however, guarantee that the small-scale violation is sufficient for supporting a macroscopic wormhole. The purpose of this paper is to connect the Casimir effect to noncommutative geometry, which also aims to accommodate small-scale effects, the difference being that these can now be viewed as intrinsic properties of spacetime. As a result, the noncommutative effects can be implemented by modifying only the energy momentum tensor in the Einstein field equations, while leaving the Einstein tensor unchanged. The wormhole can therefore be macroscopic in spite of the small Casimir effect.