Noncommutative-geometry wormholes based on the Casimir effect (2302.02244v2)

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.

• The paper proposes using noncommutative geometry and the Casimir effect to address the exotic matter requirements for creating macroscopic traversable wormholes.
• Noncommutative geometry is used to modify the energy-momentum tensor, allowing small-scale Casimir effects to potentially facilitate macroscopic wormhole construction.
• This framework also explains large radial tension at wormhole throats and suggests new research directions connecting small-scale quantum effects to large astrophysical phenomena.

Analysis of Noncommutative-Geometry Wormholes Based on the Casimir Effect

This paper explores an intriguing intersection of theoretical physics, connecting the Casimir effect with noncommutative geometry, to propose potential solutions for the existence of macroscopic traversable wormholes. The research addresses the substantial challenges associated with wormholes, particularly the exotic matter requirements dictated by quantum field theory for maintaining traversability. The paper articulates how small-scale violations of energy conditions, evidenced by the Casimir effect, may be elevated to support macroscopic phenomena in a noncommutative geometric framework.

Theoretical Foundations

The Casimir effect, typically demonstrated between closely spaced metallic plates, produces observable quantum phenomena that suggest energy condition violations necessary for wormhole solutions. This phenomenon introduces an element of exotic matter, albeit on a small scale, insufficient alone to support a macroscopic wormhole structure. Noncommutative geometry, derived from string theory, offers an alternative by reconceptualizing spacetime at a small scale, replacing point-like particles with smeared objects, effectively providing the potential to overcome divergences inherent in general relativity.

The construction of wormholes as described uses the model established by Morris and Thorne, where the spatial structure is characterized by a throat defined by specific geometric conditions. The incorporation of noncommutative geometry into this model allows the Casimir-related violations to manifest more prominently, deferring the requirement of exotic matter to modifications in the energy-momentum tensor while preserving the Einstein tensor.

Implications and Findings

The authors demonstrate that a macroscopic wormhole may be achievable without altering the overarching geometric framework of spacetime, but rather by adjusting the distribution of mass-energy using noncommutative geometry. This connects the small effects calculated within the Casimir framework to larger-scale phenomena through modified equations, extending the scale of the effects beyond what Casimir alone predicts. Specifically, the paper posits that the smearing effect due to noncommutative geometry can interpret and manipulate the uncertainties and distributions characterized by the parameter $\beta$, thus facilitating macroscopic constructs.

Furthermore, the framework also provides an explanation for the large radial tension observed at the throats of Morris-Thorne wormholes, comparing the magnitude to pressures seen within neutron star centers. The paper claims that the unique properties of noncommutative geometry, when applied to the energy-momentum tensor, are capable of rationalizing these exceptional conditions.

Future Directions and Speculations

The integration of the Casimir effect with noncommutative geometry presents promising avenues for future research in theoretical physics and cosmology, potentially offering new insights into not only the stabilization of wormholes but also other high-energy astrophysical phenomena. Further investigation into the reconciliation of small-scale quantum effects with large-scale astrophysical properties could yield innovative methods for advancing our understanding of spacetime structures. As techniques in quantum theory and geometry evolve, the predictions and models proposed in this paper can serve as a basis for both experimental and observational validation efforts in searching for evidence of observable wormholes or similar constructs.

In summary, this research opens a dialogue between small-scale quantum phenomena and potentially cosmic-scale implications, contributing a substantive layer to discussions on spacetime topology, the role of exotic matter, and the broader applicability of noncommutative geometry in physics.