[en] A possible existence of a conformal perfect fluid in the classical vacuum is investigated in this letter. It is shown, contrary to Madsen's opinion, that the scalar field stress tensor acquires a perfect fluid form even with a nonminimal coupling (ξ = 1/6) in the Einstein Lagrangian, provided the geometry is the Lorentzian analogue of the Euclidean Hawking wormhole. In addition, our T_μν equals (up to a constant factor) the vacuum expectation value of the Fulling stress tensor for a massless scalar field and Visser's one concerning transversible wormholes. On the other side of the light cone, there is a coordinate system (the dimensionally reduced Witten bubble) where the stress tensor becomes diagonal. (author). 13 refs