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Abstract

New ideas about multiplication of tensorial distributions

There is a huge need in general relativity for a consistent and useful mathematical theory defining the multiplication of tensor distributions in a geometric (diffeomorphism invariant) way. Significant progress has been made through the concept of Colombeau algebras, and construction of full Colombeau algebras on differential manifolds for scalars. Despite this, we are still lacking a similar canonical construction for arbitrary tensorial distributions. We take a new approach towards this problem, fully based on Colombeau equivalence relation. It explicitly avoids the Colombeau algebra construction, but still retains all the main advantages of Colombeau theory. It fulfills our physical intuitions, works naturally with a much more general concept of piecewise smooth manifold, and the construction is made in a canonical way.

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