The thin string limit of Cosmic Strings coupled to gravity

TL;DR

This paper explores the thin string limit of cosmic strings coupled to gravity using Colombeau's theory, showing the well-defined nature of the energy-momentum tensor and the conditions under which the conical approximation is valid.

Contribution

It introduces a Colombeau algebra framework to rigorously analyze the thin string limit and relates the deficit angle to the distributional energy-momentum tensor.

Findings

Energy-momentum tensor has a well-defined thin string limit.

Deficit angle relates to the distributional energy-momentum tensor.

Conical approximation valid outside the string's inner core.

Abstract

The thin string limit of Cosmic Strings is investigated using a description in terms of Colombeau's theory of nonlinear generalised functions. It is shown that in this description the energy-momentum tensor has a well defined thin string limit. Furthermore the deficit angle of the conical spacetime that one obtains in the limit may be given in terms of the distributional energy-momentum tensor. On the other hand it is only in the special case of critical coupling that the energy-momentum tensor defined in the Colombeau algebra is associated to a conventional distribution. The asymptotics of both the matter and gravitational field are investigated in the thin string limit and it is shown how this leads to the `conical approximation' which is valid outside the inner core of the string.