On parameters of the Levi-Civita solution

TL;DR

This paper analyzes the parameters of the Levi-Civita solution by matching it to an anisotropic fluid shell, exploring energy conditions, mass distribution, and implications for cosmic strings and horizon absence.

Contribution

It provides explicit relations for the shell's mass per unit length in terms of the Levi-Civita parameter and discusses physical implications for cosmic strings and horizon non-existence.

Findings

Energy conditions hold for 0 ≤ σ ≤ 1

Mass per unit length has a finite maximum

Results relate to cosmic string models and horizon absence

Abstract

The Levi-Civita (LC) solution is matched to a cylindrical shell of an anisotropic fluid. The fluid satisfies the energy conditions when the mass parameter $\sigma$ is in the range $0 \le \sigma \le 1$. The mass per unit length of the shell is given explicitly in terms of $\sigma$, which has a finite maximum. The relevance of the results to the non-existence of horizons in the LC solution and to gauge cosmic strings is pointed out.