Wormholes Geometry in the Einstein-Yang-Mills- Higgs Theory

We present the geometrical property of non-Abelian wormhole solutions in the Einstein-Yang-Mills-Higgs (EYMH) theory which EYMH is minimally coupled with a phantom field. In the Bogomol'nyi-Prasad-Sommerfield (BPS) limit where the Higgs self-interaction constant lambda vanishes, the wormhole spacetime undergoes the transition from a single-throat to the double-throat configuration when the gravitational strength exceeds the critical value. Beyond the BPS limit when lambda is non-vanishing, the wormholes can also possess two different types of double-throat configurations. At a certain range of lambda, these two types of double-throat configurations can exist together where it is actually a transition state between these two configurations.