Generating New Perfect Fluid Solutions from Known Ones

Stationary perfect uid con gurations of Einstein's theory of gravity are studied. It is assumed that the 4-velocity of the uid is parallel to the stationary Killing eld, and also, that the norm and the twist potential of the stationary Killing eld are functionally independent. It has been pointed out earlier by one of us (I.R.) that for these perfect uid geometries some of the basic eld equations are invariant under an SL(2;IR) transformation. Here it is shown that this transformation can be applied to generate new perfect uid solutions from existing known ones only for the case of barotropic equation of state +3p = 0. In order to study the e ect of this transformation, its application to known perfect uid solutions is presented. Although the equation of state has to remain + 3p = 0, the new perfect uid geometries possess an extra parameter associated with the one-parameter subclass of the `e ective' SL(2;IR) transformations. As a compensation for the very restricted form of the equation of state, some of the new solutions are algebraically more general than the original ones we started with. PACS number: 04.20.Jb, 04.40.+c