Solutions for the general cylindrically symmetric stationary dust model

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Abstract
For a dust‐filled space–time possessing cylindrical symmetry, the field equations form an underdetermined set. As demonstrated by King [Commun. Math. Phys. 38, 157 (1974)], by carefully selecting a function it is possible to generate solutions which are either well‐behaved or are characterized by one of a number of different types of singularity. The three particular choices for the functions we take produce two nonsingular solutions and one with a Weyl singularity.

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