SMOOTH AND DISCONTINUOUS SIGNATURE CHANGE IN GENERAL-RELATIVITY - COMMENT

Kossowski and Kriele derived boundary conditions on the metric at a su rface of signature change. We point out that their derivation is based not only on certain smoothness assumptions but also on a postulated f orm of the Einstein field equations. Since there is no canonical form of the field equations at a change of signature, their conclusions are not inescapable. We show here that a weaker formulation is possible, in which less restrictive smoothness assumptions are made, and (a slig htly different form of) the Einstein field equations are satisfied. In particular, in this formulation it is possible to have a bounded ener gy-momentum tensor at a change of signature without satisfying their c ondition that the extrinsic curvature vanish.