Abstract
The physical meaning of the Levi-Civita spacetime, for some "critical" values of the parameter σ, is discussed in the light of gedanken experiments performed with gyroscopes circumscribing the axis of symmetry. The fact that σ = 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 φ as an angle coordinate for any value of σ, appears to be the origin of difficulties.
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