On the interpretation of cylindrically symmetric Levi-Civita spacetime for 0<sigma<infinity

TL;DR

This paper analyzes the Levi-Civita spacetime for all positive sigma values, revealing coordinate interpretation changes at sigma=1/2, and presents geodesic and physical source analyses consistent with energy conditions and horizon absence.

Contribution

It provides a comprehensive interpretation of Levi-Civita spacetime across all sigma values, including coordinate switch at sigma=1/2 and a compatible physical source.

Findings

Coordinate interpretation switches at sigma=1/2

Physical source satisfies energy conditions

No event horizon exists in the solution

Abstract

We study Levi-Civita metric for values of its sigma parameter in the range 0< sigma<infinity. We show that the value sigma=1/2 makes the axial and angular coordinates switch meaning. We present its geodesics and a physical source satisfying the energy conditions for all the range of sigma. This source allows us to obtain an energy per unit length which agrees with the behaviour of the geodesics and the fact that the solution has no event horizon.