All flow-stationary cylindrically symmetric solutions of the Einstein field equations for a rotating isentropic perfect fluid

In previous papers by the author a class of flow-stationary cylindrically symmetric solutions of the Einstein field equations for a rotating isentropic perfect fluid was found. The present paper shows how all such solutions may be obtained by methods very similar to those used previously. The solutions depend on one variable and contain one completely arbitrary function f of that variable. The choice of a definite form of f corresponds to fixing the equation of state. After this is fixed, the enthalpy per unit rest-energy of the fluid, H, is determined by a linear homogeneous differential equation of second order, and all the other components of the metric are algebraically determined in terms of f and H.