Generating 4-dimensional Wormholes with Yang-Mills Casimir Sources

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.