Levi-Civita Solutions Coupled with Electromagnetic Fields

TL;DR

This paper investigates Levi-Civita solutions with electromagnetic fields, analyzing their properties, limits, and sources, revealing how electromagnetic fields influence the physical realization of these solutions via cylindrical thin shells.

Contribution

It provides a detailed analysis of Levi-Civita solutions coupled with electromagnetic fields, including their limits, physical interpretations, and the conditions under which they can be sourced by thin shells.

Findings

Vacuum solutions with σ ≥ 0 can be generated by physically acceptable thin shells.

Magnetic fields allow shells for σ ≥ 1/√8 or σ ≤ -1/√8, electric fields do not.

Electromagnetic fields significantly alter the source conditions of Levi-Civita solutions.

Abstract

The local and global properties of the Levi-Civita (LC) solutions coupled with an electromagnetic field are studied and some limits to the vacuum LC solutions are given. By doing such limits, the physical and geometrical interpretations of the free parameters involved in the solutions are made clear. Sources for both the LC vacuum solutions and the LC solutions coupled with an electromagnetic field are studied, and in particular it is found that all the LC vacuum solutions with $\sigma \ge 0$ can be produced by cylindrically symmetric thin shells that satisfy all the energy conditions, weak, dominant, and strong. When the electromagnetic field is present, the situation changes dramatically. In the case of a purely magnetic field, all the solutions with $\sigma \ge 1/\sqrt{8}$ or $\sigma \le - 1/\sqrt{8}$ can be produced by physically acceptable cylindrical thin shells, while in the case of a purely electric field, no such shells are found for any value of $\sigma$.