Stationary and Axisymmetric Perfect Fluids with one Conformal Killing Vector

We study the stationary and axisymmetric non-convective differentially rotating perfect-fluid solutions of Einstein’s field equations admitting one conformal symmetry. We analyse the two inequivalent Lie algebras not exhaustively considered in [1] and show that the general solution for each Lie algebra depends on one arbitrary function of one of the coordinates while a set of three ordinary differential equations for four unknowns remains to be solved. The conformal Killing vector of these solutions is necessarily homothetic. We summarize in a table all the possible solutions for all the allowed Lie algebras and also add a corrigendum to an erroneous statement in [1] concerning the differentially rotating character of one of the solutions presented. ∗Also at Laboratori de F́ısica Matemàtica, IEC, Barcelona.