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The vacuum line element inside an infinitely long rotating hollow cylinder is the usual flat space line element. It is fitted in a most general way to the general cylindrical vacuum field outside at the singular hypersurface R o = const, representing the infinitely thin hollow cylinder. With the use of the jump conditions at R o = const the surface densities τ x μ , of which the energy-momentum-stress tensor τ^ of the shell consists, are calculated. The physical properties of the cylinder, as derived from the eigenvalues and -vectors of τj, and the generated gravitational field are discussed in full detail.

The general stationary vacuum gravitational field of cylindrical symmetry as recently found by Davies and Caplan is even static. The possible Petrov types of the Riemann tensor are I, D or O. In spacelike infinity the spacetime becomes necessarily flat.

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