CHANGE OF SIGNATURE IN CLASSICAL RELATIVITY

We point out that the classical Einstein field equations, suitably interpreted, allow a change of signature of spacetime. Specific examples of such changes are constructed in the case of Robertson-Walker geometries. We obtain classical solutions that have properties similar to those obtained in quantum cosmologies obeying the Hartle-Hawking 'no boundary' condition: these singularity-free universes have no beginning, but they do have an origin of time. They can be regarded either as classical analogues of the quantum cosmology results, or as classical solutions where a quantum cosmology era is avoided.