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.
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