The Static Cylinder, Gyroscopes and the C-Metric

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 circumventing 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 at the origin of difficulties.

Cylindrical systems in general relativity

“…The existence and uniqueness of global solutions are shown for rather general fluid EoS admitting nonvanishing density at zero pressure. In [188], it is shown that conformally flat internal solutions cannot be matched to an LC exterior.…”

Quantum singularity of Levi-Civita spacetimes

“…On the other hand, one can interpret the metric with σ = −1/2 as the gravitational field produced by an infinite sheet of negative mass density (an idea also first proposed by Gautreau and Hoffmann [18]). However, this case is also problematic [15,17,16]. The metric…”

“…The interpretation of this spacetime as one caused by an infinite plane of negative mass density comes from the fact that test particles are repelled from the r = 0 plane and the fact that "the Gaussian curvature of spacelike 'eigensurfaces' is zero" [18]. This is a reasonable interpretation; the "problem" comes from interpreting both σ = 1/2 and σ = −1/2 as planes of infinite (positive/negative) mass density as one is singularity-free and the other has a curvature singularity [17,16]. We will now study the quantum singularity properties of these spacetimes for various parameter values in the following sections.…”

On the gravitomagnetic effects in cylindrically symmetric space–times

“…On the other hand, since Ω i describes the rate of rotation with respect to the proper time at any point at rest in the rotating frame, relative to the local compass of inertia, then −Ω i describes the rotation of the compass of inertia (the gyroscope) with respect to the rotating frame. Applying (9) to the original frame of (1), with t = t ′ , r = r ′ and z = z ′ , we cast (1) into the canonical form (10), and obtain (see (43) in [5])…”