Rotationally symmetric clusters with zero net angular momentum

The Levi–Civita space–time

“…Using the solution for a cluster constituted by dust particles with constant angular velocity and zero net angular momentum, obtained firstly by Teixeira and Som [1], and matching it with the Levi-Civita metric, we found that the parameter σ in this case should be smaller or equal than . Considering σ as the gravitational mass per unit length this limit is in agreement with the result of Lathrop and Orsene [4].…”

“…They also deduced a relation between the gravitational mass and the sum of the free particles masses of their clusters. Another cluster solution was obtained by Teixeira and Som [1]. They suposed a constant angular velocity for the dust particles.…”

“…This section is subdivided into two subsections, where we present a new cylindrical cluster solution for homogeneous dust, found by us, and the Teixeira and Som [1] cluster solution.…”

Perfect-Fluid Sources for the Levi-Civita Metric II

“…Although the Levi-Civita exterior metric was derived in 1919, the interior field equations were not investigated until 1958 when Marder [2] obtained a solution representing an anisotropic fluid. Other solutions representing clusters of rotating particles have been given [3][4][5][6]. The problem for static perfect fluid interior was first solved in 1977 by Evans [7] and quite a few number of solutions, some of them overlapping, have been published since then [8][9][10][11][12][13].…”

The Static Cylinder, Gyroscopes and the C-Metric

“…The absence of circular test particle orbits for σ > 1/4, and the fact that most of the known material sources for LC, [4], [5], [6], [11] require σ ≤ 1/4, led to think that LC describes the field of a cylinder only if σ ranges within the (0,1/4) interval.…”