We extend the construction of the authors’ paper of 2002 by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces… (More)

Generalized tensor analysis in the sense of Colombeau’s construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several… (More)

where (u, v) and (x, y) is a pair of null and (transverse) Cartesian coordinates respectively, and f denotes the profile function subject to the field equations. Hence the spacetime is flat… (More)

The concept of generalized functions taking values in a differentiable manifold ([15, 19]) is extended to a functorial theory. We establish several characterization results which allow a global… (More)

Colombeau’s construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis and… (More)

Colombeau’s construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis and… (More)

In this paper we review the extent to which one can use classical distribution theory in describing solutions of Einstein's equations. We show that there are a number of physically interesting cases… (More)

We compare two approaches to Semi-Riemannian metrics of low regularity. The maximally “reasonable” distributional setting of Geroch and Traschen is shown to be consistently contained in the more… (More)

Based on the concept of manifold valued generalized functions we initiate a study of nonlinear ordinary differential equations with singular (in particular: distributional) right hand sides in a… (More)

We present a geometric approach to diffeomorphism invariant full Colombeau algebras which allows a particularly clear view of the construction of the intrinsically defined algebra Ĝ(M) on the… (More)