  Stationary perfect-fluid configurations of Einstein's theory of gravity are
studied. It is assumed that the 4-velocity of the fluid is parallel to the
stationary Killing field, and also that the norm and the twist potential of the
stationary Killing field are functionally independent. It has been pointed out
earlier by one of us (I.R.) that for these perfect-fluid geometries some of the
basic field equations are invariant under an $SL(2,R)$ transformation. Here it
is shown that this transformation can be applied to generate possibly new
perfect-fluid solutions from existing known ones only for the case of
barotropic equation of state $\rho+3p=0$. In order to study the effect of this
transformation, its application to known perfect-fluid solutions is presented.
In this way, different previously known solutions could be written in a singe
compact form. A new derivation of all Petrov type D stationary axisymmetric
rigidly rotating perfect-fluid solutions with an equation of state
$\rho+3p=constant$ is given in an appendix.
