Non-Abelian Wormholes Threaded by a Yang-Mills-Higgs Field beyond the BPS Limit

We construct numerically the symmetric non-Abelian wormholes which are supported by a phantom field in the Einstein-Yang-Mills-Higgs theory beyond Bogomol'nyi-Prasad-Sommerfield (BPS) limit where the Higgs self-interaction constant $\lambda$ is non-vanishing. Analogous to the BPS limit, the probe limit is the Yang-Mills-Higgs field in the background of the Ellis wormhole when the gravity is switched off. In the presence of gravity, the wormhole solutions possess the Yang-Mills-Higgs hair where families of hairy wormholes solutions emerge from the Ellis wormhole when the gravitational coupling constant increases. In contrast to the BPS limit, the properties of wormholes change drastically when the gravitational strength approaches a critical value for a fixed $\lambda$. The hairy wormholes possess two types of double throat configurations. The first type is wormholes that develop the double throat when the gravitational strength almost approaches the critical value for lower $\lambda$, whereas the second type is wormholes that exhibit the double throat for a certain range of gravitational strength for higher $\lambda$. These two types of double throat configurations can coexist for a certain range of $\lambda$ where it is a transition process for first type double throat disappears gradually and the second type double throat becomes dominant.