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The Levi-Civita space-time. (English) Zbl 0842.53056

Summary: Two exact solutions of Einstein’s field equations corresponding to a cylinder of dust with not zero angular momentum are considered. In one of the cases, the dust distribution is homogeneous, whereas in the other, the angular velocity of dust particles is constant [A. F. F. Teixeira and M. M. Som, Nuovo Cimento B 21, 64 (1974)]. For both solutions the junction conditions to the exterior static vacuum Levi-Civita space-time are studied. From this study we find an upper limit for the energy density per unit length \(\sigma\) of the source for both cases. Thus the homogeneous cluster provides another example [W. B. Bonnor and M. A. P. Martins, Classical Quantum. Gravity 8, No. 4, 727-738 (1991); J. D. Lathrop and M. S. Orsene, J. Math. Phys. 21, No. 1, 152-153 (1980)] where the limit of \(\sigma\) is \({1\over 4}\). It is also found that the cluster of homogeneous dust has a superior limit for its radius, depending on the constant volumetric energy density \(\rho_0\).

MSC:

53Z05 Applications of differential geometry to physics
83C15 Exact solutions to problems in general relativity and gravitational theory
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References:

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