Tensor distributions on signature-changing space-times (Q1584758)

The formalism of tensor distributions is applied to signature-changing space-times. It is shown that, for both continuous and discontinuous signature-change, covariant differentiation can be defined on a class of important tensor distributions. The definitions for ordinary and covariant differentiations depend on an auxiliary volume element rather than on a metric tensor. This avoids introducing irregularities when the metric tensor and connection are not smooth. Finally, some illustrative examples are given.