Euclidean non-vacuum wormholes in Brans－Dicke theory

The Brans－Dicke theory is investigated in which the Pauli metric is identified to be a physical spacetime metric. The solutions of a wormhole are obtained in Brans－Dicke theory with a relativistic radiation field for ω>-3/2. However, it is found that one cannot construct a wormhole in the presence of a 3-form axion field.