Covariant change of signature in classical relativity

This paper gives a covariant formalism enabling investigation of the possibility of change of signature in classical General Relativity, when the geometry is that of a Robertson-Walker universe. It is shown that such changes are compatible with the Einstein field equations, both in the case of a barotropic fluid and of a scalar field. A criterion is given for when such a change of signature should take place in the scalar field case. Some examples show the kind of resulting exact solutions of the field equations.