Generalised Functions and Distributional Curvature of Cosmic Strings

TL;DR

This paper introduces a novel invariant method using Colombeau's generalized functions to assign distributional curvature to low-differentiability spacetimes, demonstrating that the curvature of a cone is a delta function.

Contribution

It develops a new invariant approach for distributional curvature using Colombeau's functions, applicable to low differentiability space-times, and shows curvature of a cone equals a delta function.

Findings

Curvature of a cone is equivalent to a delta function.

The method remains valid under small perturbations.

Provides a consistent way to handle curvature in low-regularity geometries.

Abstract

A new method is presented for assigning distributional curvature, in an invariant manner, to a space-time of low differentiability, using the techniques of Colombeau's `new generalised functions'. The method is applied to show that curvature of a cone is equivalent to a delta function. The same is true under small enough perturbations.