A class of space-times of non-rigidly rotating dust

We find a class of exact solutions of differentially rotating dust in the framework of General Relativity. There exist asymptotically flat space-times of the flow with positive mass function that for radii sufficiently large is monotonic and tends to zero at infinity. Some of the space-times may have non-vanishing total angular momentum. The flow is essentially different from another exactly solvable flow described by van Stockum line element.