da Silva, M. F. A.; Herrera, L.; Paiva, F. M.; Santos, N. O. The Levi-Civita space-time. (English) Zbl 0842.53056 J. Math. Phys. 36, No. 7, 3625-3631 (1995). 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 \(\rho_0\). Cited in 17 Documents MSC: 53Z05 Applications of differential geometry to physics 83C15 Exact solutions to problems in general relativity and gravitational theory Keywords:exact dust solutions; junction conditions; energy density PDFBibTeX XMLCite \textit{M. F. A. da Silva} et al., J. Math. Phys. 36, No. 7, 3625--3631 (1995; Zbl 0842.53056) Full Text: DOI arXiv References: [1] Levi-Civita T., Rend. Ace. Lincei 26 pp 307– (1917) [2] DOI: 10.2307/1968902 · Zbl 0023.42501 · doi:10.2307/1968902 [3] DOI: 10.1017/S0305004100036549 · doi:10.1017/S0305004100036549 [4] DOI: 10.1007/BF02737438 · doi:10.1007/BF02737438 [5] DOI: 10.1063/1.524340 · doi:10.1063/1.524340 [6] DOI: 10.1063/1.523404 · doi:10.1063/1.523404 [7] DOI: 10.1007/BF02710947 · doi:10.1007/BF02710947 [8] DOI: 10.1088/0264-9381/8/4/016 · doi:10.1088/0264-9381/8/4/016 [9] DOI: 10.1088/0264-9381/9/9/012 · doi:10.1088/0264-9381/9/9/012 [10] Stela J., Acta Phys. Pol. B 21 pp 843– (1990) [11] DOI: 10.1098/rspa.1958.0058 · Zbl 0080.21801 · doi:10.1098/rspa.1958.0058 [12] DOI: 10.1017/S0370164600013699 · Zbl 0016.28302 · doi:10.1017/S0370164600013699 [13] DOI: 10.1103/PhysRevD.9.2203 · doi:10.1103/PhysRevD.9.2203 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.