Some Collapsing Cylinders and their Exterior Vacuum Metrics in General Relativity

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Abstract
A cylindrical form of the Friedman metric is used to obtain nonstatic infinite cylinders of incoherent fluid. The vacuum metrics exterior to the cylinders are determined from the hypothesis that the metric tensor and its first partial derivatives be continuous. This hypothesis is applied by requiring the continuity of the first and second fundamental forms of the boundaries of the cylinders. The exterior metrics are nonstatic and may be expressed in the Einstein‐Rosen form, and equations governing their behavior are derived. It is found that the exterior metric carries a flux of gravitational ``C energy,'' the direction of which in the Einstein‐Rosen frame is the same as that of the surface of the cylinders.

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