Rotating cylinders and the possibility of global causality violation

In 1936 van Stockum solved the Einstein equations $G_{\mu \nu }=-8\pi T_{\mu \nu }$ for the gravitational field of a rapidly rotating infinite cylinder. It is shown that such a field violates causality, in the sense that it allows a closed timelike line to connect any two events in spacetime. This suggests that a finite rotating cylinder would also act as a time machine.