THE LEVI-CIVITA SPACE-TIME

Two exact solutions of Einstein's field equations corresponding to a c ylinder of dust with net zero angular momentum are considered. In one of the cases, the dust distribution is homogeneous, whereas in the oth er, the angular velocity of dust particles is constant [Nuovo Cimento B 21, 64 (1974)]. For both solutions the junction conditions to the ex terior static vacuum Levi-Civita space-time were studied. From this st udy we find an upper limit for the energy density per unit length a of the source equals 1/4 for both cases. Thus the homogeneous cluster pr ovides another example [Class. Quant. Grav. 8, 727 (1991); J. Math. Ph ys. 27, 152 (1980)] where the limit of sigma is 1/4. It was also found that the cluster of homogeneous dust has a superior limit for its rad ius, depending on the constant volumetric energy density rho(0). (C) 1 995 American Institute of Physics.