Abstract
Assuming a particular form of metric containing seven constant parameters, Einstein's equations are solved for a perfect fluid in steady cylindrically symmetric rigid-body rotation about a regular axis, the equation of state being where . The resultant metric contains two free parameters. The angular velocity of the vortex is finite, and the motion in the radially infinite cylinder is without shear. The pressure p and density are also finite, vanishing at infinity. There are no singularities in the spacetime, which is of Petrov type I except for the case which is of type D. Some other cases, falling outside the range of given above, are discussed briefly.
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