The Levi-Civita space–time as a limiting case of the γ space–time

Abstract

It is shown that the Levi-Civita metric can be obtained from a family of the Weyl metric, the γ metric, by taking the limit when the length of its Newtonian image source tends to infinity. In this process a relationship appears between two fundamental parameters of both metrics. * Postal address: Apartado 80793,

Thin-shell wormholes supported by total normal matter

“…We note that −∞ < δ < ∞ such that δ = 0 corresponds to a flat spacetime, and with δ = 1 one finds the Schwarzschild black hole solution with the horizon located at x = 1. For the case δ = 1 the hypersurface x = 1 is a true curvature singularity (naked singularity) [45][46][47][48][49]. As we shall see, the asymptotic behavior of the ZV spacetime for x → ∞ and δ > 1 is of our interest.…”

Static Cylindrical Symmetry and Conformal Flatness

“…We number the coordinates x 0 = t, x 1 = r, x 2 = z and x 3 = φ and we choose the fluid being at rest in this coordinate system, hence from (2) and (3) we have…”

“…The fact that there are two parameters while in its counterpart, Newtonian theory, has only one parameter looks a sufficient justification for deserving more research. But the importance of its research goes further if one notices the close link between Levi-Civita, γ and Schwarzschild spacetimes [2] and its peculiar properties. Besides, there has been renewed interest in cylindrically symmetric sources in relation with different, classical and quantum, aspects of gravitation (see [3] and references therein).…”

Can we measure structures to a precision better than the Planck length?

“…The gravitational field of a line mass of finite length is the γ-metric and in the limit of infinite extension one obtains the Levi-Civita metric [19]. In cylinder coordinates r, z, φ, it takes the form [20] …”