Global algebras of nonlinear generalized functions with applications in general relativity

TL;DR

This paper reviews the development of Colombeau algebras of generalized functions, highlighting recent advances in diffeomorphism invariance and applications to general relativity where traditional distribution theory faces limitations.

Contribution

It provides a comprehensive overview of the evolution of Colombeau algebras and discusses their recent extensions and applications in general relativity.

Findings

Diffeomorphism invariant algebras have been developed.

Applications in general relativity address distribution theory limitations.

Survey of recent advances in generalized function algebras.

Abstract

We give an overview of the development of algebras of generalized functions in the sense of Colombeau and recent advances concerning diffeomorphism invariant global algebras of generalized functions and tensor fields. We furthermore provide a survey on possible applications in general relativity in light of the limitations of distribution theory.