Metrics with distributional curvature

TL;DR

This paper introduces semi-regular metrics with distributional curvature, extending Geroch and Traschen's regular metrics, and analyzes specific semi-regular examples like wedge removal in Minkowski space and a traveling wave metric.

Contribution

It generalizes the class of regular metrics to semi-regular metrics and provides detailed analysis of new examples with distributional curvature.

Findings

Semi-regular metrics include non-regular examples like wedge removal and traveling wave metrics.

Distributional curvature can be well-defined for a broader class of metrics.

The paper expands understanding of metrics with distributional curvature in geometric analysis.

Abstract

This paper considers metrics whose curvature tensor makes sense as a distribution. A class of such metrics, the regular metrics, was defined and studied by Geroch and Traschen. Here, we generalize their definition to form a wider class: semi-regular metrics. We then examine in detail two metrics that are semi-regular but not regular: (i) Minkowski spacetime minus a wedge and (ii) a certain traveling wave metric.