The static cylinder, gyroscopes, the C metric, and all that

TL;DR

This paper explores the physical interpretation of Levi-Civita spacetime at critical parameter values through gedanken experiments with gyroscopes, linking it to the C metric and addressing angular variable issues.

Contribution

It provides a new analysis of Levi-Civita spacetime's physical meaning at specific parameters using thought experiments and incorporates the C metric into this discussion.

Findings

Sigma=1/2 corresponds to flat space in an accelerated frame

Interpretation of phi as an angle variable causes difficulties

Connections between Levi-Civita spacetime and the C metric are established

Abstract

The physical meaning of the Levi-Civita spacetime for some "critical" values of the parameter sigma, is discussed in the light of gedanken experiments performed with gyroscopes circumventing the axis of symmetry. The fact that sigma=1/2 corresponds to flat space described from the point of view of an accelerated frame of reference, led us to incorporate the C metric into discussion. The interpretation of phi as an angle variable for any value of sigma, appears to be at the origen of difficulties.