Distributional curvature of time-dependent cosmic strings

TL;DR

This paper employs Colombeau's theory to analyze the distributional curvature of a time-dependent radiating cosmic string, deriving its mass per unit length and comparing it with the mass at null infinity to support energy conservation.

Contribution

It introduces a novel application of Colombeau's theory to compute distributional curvature for dynamic cosmic strings and links local and global energy measures.

Findings

Calculated the distributional curvature at the rotation axis.

Derived the mass per unit length of the cosmic string.

Provided evidence for a global energy conservation law.

Abstract

Colombeau's theory of generalised functions is used to calculate the contributions, at the rotation axis, to the distributional curvature for a time-dependent radiating cosmic string, and hence the mass per unit length of the string source. This mass per unit length is compared with the mass at null infinity, giving evidence for a global energy conservation law.