Barotropic perfect fluid in steady cylindrically symmetric rotation

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 p = (gamma - 1)mu where gamma = constant (3/2 < gamma less than or equal to 2). 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 mu are also finite, vanishing at infinity. There are no singularities in the spacetime, which is of Petrov type I except for the case gamma = 2 which is of type D. Some other cases, falling outside the range of gamma given above, are discussed briefly.