Generating 4-dimensional Wormholes with Yang-Mills Casimir Sources

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 $x=mr\ll 1$, 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 $0\le m\le 0.20$. 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 $0.16\le m\le 0.18$, we will have a stable solution that satisfies all traversability conditions.

16 pages, 9 figures, Improved and accepted version for publication in Annals of Physics