On the traversable Yukawa-Casimir wormholes

TL;DR

This paper demonstrates that traversable wormholes sourced by Casimir energy can exist in all dimensions greater than three, and explores how Yukawa-type modifications influence their properties without relying on previous restrictive assumptions.

Contribution

The authors extend Casimir-based traversable wormhole solutions to all dimensions >3 and analyze the effects of Yukawa corrections without previous questionable premises.

Findings

Traversable wormholes can be constructed with Casimir energy in all dimensions greater than three.

Yukawa-type corrections allow for wormholes with adjustable gravitational properties.

A limitation on the shielding factor was identified in the constant case, unlike in previous models.

Abstract

Wormholes (WH) require negative energy, and therefore an exotic matter source. Since Casimir energy is negative, it has been speculated as a good candidate to source that objects a long time ago. However only very recently a full solution for $D = 4$ has been found by Garattini, thus the Casimir energy can be a source of traversable WHs. In the manuscript published by the authors, we show that this solution is possible for all space-time of dimension $D > 3$. Recently, Garattini sought to analyze the effects of Yukawa-type terms on shape functions and obtained promising results. However, it assumes reasonably questionable premises when establishing a non-homogeneity in the Equation of State, when assuming a fixation between the constants that is only observed in the usual model and when considering the Zero Tidal Condition, not observed in Casimir's wormholes. In this work, we study the effects generated by Yukawa-type corrective factors on traversable wormhole solutions generated by Casimir energy without assuming such premises. We observe that, in addition to being possible to build traversable wormholes that satisfy all the necessary conditions, it is possible to obtain an adequate fixation of the constants in order to recover the standard case without a double limit. It was observed that, in the global and constant cases, it is possible to set a value in the shielding parameter that makes the wormhole generate a repulsive gravitational force. Finally, we observed that in the constant case there was a limitation for the shielding factor, something not observed in the original article.