Wormhole solutions in the Einstein-Yang-Mills-Higgs system: Solution of first order equations for \(G=SU(2)\) (Q1819394)

For an SU(2) Einstein-Yang-Mills-Higgs model we study the extreme wormhole solutions. We use an iterative method based on expansion in the radial distance N 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 charge b and the electric charge e of the hole satisfy \(b=1/e\).