The solutions of wormhole in Brans-Dicke theory

Abstract

We discuss wormhole solution in the Brans-Dicke theory with existence of relativistic radiation field. The solutions of wormhole are obtained in the Einstein frame. When the dilaton field σ = const, the solution of wormhole should be reduced to the well-known Tolman wormhole. Euclidean wormhole solution also has been obtained in the Einstein frame when σ ≠ const. For the comparison, we also derive the wormhole solution in the Jordan frame with existence of relativistic radiation field. However, the two frames, the Einstein frame and the Jordan frame, are not physically equivalent.