Generating 4-dimensional Wormholes with Yang-Mills Casimir Sources

TL;DR

This paper introduces a novel 4D wormhole solution in General Relativity supported by Casimir vacuum fluctuations, analyzing its stability, traversability, and energy conditions with a focus on the Casimir mass parameter.

Contribution

It presents the first wormhole solution in 4D supported by Casimir effects, including stability and traversability analysis within a perturbative framework.

Findings

Stable wormhole solutions exist for Casimir mass between 0.16 and 0.18.

All energy conditions are violated, consistent with wormhole physics.

Traversability conditions are satisfied for Casimir mass up to 0.20.

Abstract

This work presents a new wormhole solution in General Relativity supported by the quantum vacuum fluctuations of the Casimir effect between perfect chromometallic mirrors in $(3+1)$ dimensions, which was recently fitted using first-principle numerical simulations. Initially, we employ a perturbative approach for $x = m r \ll 1$, where $m$ represents the Casimir mass. This approach has proven to be a reasonable approximation when compared with the exact case in this regime. To find well-behaved redshift functions, we impose constraints on the free parameters. As expected, this solution recovers the electromagnetic-like Casimir solution for $m = 0$. Analyzing the traversability conditions, we graphically find that all will be satisfied for $ 0 \leq m \leq 0.20$. On the other hand, all the energy conditions are violated, as usual in this context. Stability from Tolman-Oppenheimer-Volkov (TOV) equation is guaranteed for all $r$ and from the speed of sound for $0.16 \le m \le 0.18$. Therefore, for $0.16 \leq m \leq 0.18$, we will have a stable solution that satisfies all traversability conditions.