A Petrov-type I and generically asymmetric rotating dust family

The general line element corresponding to the family of algebraically general, gravito-electric, expanding, rotating dust models with one functionally independent zero-order Riemann invariant is constructed. The isometry group is at most one dimensional but generically trivial. It is shown that the asymmetric solutions with constant ratio of energy density and vorticity amplitude provide first examples of Petrov-type I spacetimes for which the Karlhede classification requires the computation of the third covariant derivative of the Riemann tensor. (fast track communication)