Hairy wormholes and Bartnik-McKinnon solutions

We consider Lorentzian wormholes supported by a phantom field and threaded by nontrivial Yang-Mills fields, which may be regarded as hair on the Ellis wormhole. Like the Bartnik-McKinnon solutions and their associated hairy black holes, these hairy wormholes form infinite sequences, labeled by the node number k of their gauge field function. We discuss the throat geometry of these wormholes, showing that odd-k solutions may exhibit a double throat, and evaluate their global charges. We analyze the limiting behavior exhibited by wormhole solutions as the gravitational coupling becomes large. The even-k solutions approach smoothly the Bartnik-McKinnon solutions with k/2 nodes, while the odd-k solutions develop a singular behavior at the throat in the limit of large coupling. In the limit of large k, on the other hand, an embedded Abelian wormhole solution is approached, when the throat is large. For smaller throats the extremal Reissner-Nordstrom solution plays a fundamental role in the limit.