On the Geroch-Traschen class of metrics

TL;DR

This paper compares two frameworks for low-regularity semi-Riemannian metrics, demonstrating that Geroch-Traschen metrics are encompassed within the broader Colombeau distributional geometry, thus unifying different approaches.

Contribution

It shows that the Geroch-Traschen class of metrics is a special case within the more general Colombeau distributional framework, clarifying their relationship.

Findings

Geroch-Traschen metrics are contained in Colombeau's framework.

The Colombeau approach generalizes the Geroch-Traschen class.

Unified understanding of low-regularity metrics achieved.

Abstract

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 general setting of nonlinear distributional geometry in the sense of Colombeau.