The Levi-Civita spacetime

Details The Levi-Civita spacetime The Levi-Civita spacetime

1996-07-23

arxiv.org/abs/gr-qc/9607058v1

J.Math.Phys. 36 (1995) 3625-3631

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

10.1063/1.530986

We consider two exact solutions of Einstein's field equations corresponding to a cylinder of dust with net zero angular momentum. In one of the cases, the dust distribution is homogeneous, whereas in the other, the angular velocity of dust particles is constant [1]. For both solutions we studied the junction conditions to the exterior static vacuum Levi-Civita spacetime. From this study we find an upper limit for the energy density per unit length $\sigma$ of the source equal ${1\over 2}$ for the first case and ${1\over 4}$ for the second one. Thus the homogeneous cluster provides another example [2] where the range of $\sigma$ is extended beyond the limit value ${1\over 4}$ previously found in the literature [3,4]. Using the Cartan Scalars technics we show that the Levi-Civita spacetime gets an extra symmetry for $\sigma={1\over 2}$ or ${1\over 4}$. We also find that the cluster of homogeneous dust has a superior limit for its radius, depending on the constant volumetric energy density $\rho_0$.

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