Generating 4-dimensional wormholes with Yang–Mills Casimir sources

Abstract

This work presents a new static and spherically symmetric traversable wormhole solution in General Relativity, which is supported by the quantum vacuum fluctuations associated with the Casimir effect of the Yang–Mills field confined between perfect chromometallic mirrors in $(3+1)$ dimensions, recently fitted using first-principle numerical simulations. Initially, we employ a perturbative approach for $x=mr\ll 1$, where $m$ represents the Casimir mass and $r$ is the radial coordinate. 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 are satisfied for $0\le m\le 0.17$. On the other hand, all the energy conditions are violated, as usual in this context due to the quantum origin of the source. 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 $0.16\le m\le 0.17$, we will have a stable solution that satisfies all traversability conditions.