The Levi-Civita spacetime as a limiting case of the Gamma spacetime

TL;DR

This paper demonstrates that the Levi-Civita spacetime can be derived as a limiting case of the Gamma spacetime by taking the source length to infinity, revealing a connection between their fundamental parameters.

Contribution

It establishes a new link between Levi-Civita and Gamma metrics through a limiting process, enhancing understanding of their geometric relationship.

Findings

Levi-Civita metric is a limit of the Gamma metric as source length tends to infinity.

A relationship between parameters of both metrics is identified.

The process clarifies the geometric connection between the two spacetimes.

Abstract

It is shown that the Levi-Civita metric can be obtained from a family of the Weyl metric, the Gamma metric, by taking the limit when the length of its Newtonian image source tends to infinity. In this process a relationship appears between two fundamental parameters of both metrics.