The static cylinder, gyroscopes and the C-metric

The physical meaning of the Levi-Civita spacetime, for some "critical" valu es of the parameter a, is discussed in the light of gedanken experiments pe rformed with gyroscopes circumscribing the axis of symmetry. The fact that sigma = 1/2 corresponds to flat space described from the point of view of a n accelerated frame of reference, led us to incorporate the C-metric into d iscussion. The interpretation of phi as an angle coordinate for any value o f a, appears to be the origin of difficulties.