Wormhole solutions in the Einstein-Yang-Mills-Higgs system: Solution of first-order equations forG=SU(2)

For anSU(2) Einstein-Yang-Mills-Higgs model we study the extreme wormhole solutions. We use an iterative method based on expansion in the radial distanceN from the boundary of the hole. Here we present the nontrivial solutions of the first-order equations. They give useful information about existing extremal wormholes. Especially we note that although the zero-order solution which we use is abelian, this is not the case for all solutions of first-order equations. The method employed in solving these equations is to expand all first-order fields in the appropriate generalized harmonics. We find a non-abelian solution if the value of the Higgs scalar at the horizon is equal to the Planck mass and if the magnetic chargeb and the electric chargee of the hole satisfyb=1/e.Work supported by Schweizerischer Nationalfonds.