NEW IDEAS ABOUT MULTIPLICATION OF TENSORIAL DISTRIBUTIONS

There is a significant need in general relativity for a consistent and useful mathematical theory defining the multiplication of tensor distributions in a geometric (diffeomorphism invariant) way. This need is just a need of using the language of distributions in nonlinear and geometrically formulated physics. The goal is to be able to look for interesting solutions in a much wider class of objects than is a class of smooth tensor fields (possibly to deal with singularities as well), but in our view, there is also a really deep physical meaning in working with distributions rather than with smooth tensor fields. In general, distributions express in a much more intuitive way the “physical” objects than does the language of functions.