Nonexistence theorems for asymptotically Euclidean Einstein-matter solutions

Some nonexistence results are established for "Euclidean wormholes," i.e., solutions of the Euclidean version of the Einstein-matter-field equations describing four-dimensional geometries with asymptotically Euclidean regions and matter fields satisfying appropriate falloff conditions in these regions. Our main result shows that no such solutions exist if the matter fields are conformally invariant. We also point out that in many nonconformally invariant cases [such as a scalar field with potential V(φ) satisfying φdV/dφ>0] the matter-field equations alone suffice to rule out the possibility of solutions.