Algebraically general, gravito-electric rotating dust

The class of gravito-electric, algebraically general, rotating `silent’ dust space-times is studied. The main invariant properties are deduced. The number $t_0$ of functionally independent zero-order Riemann invariants satisfies $1\le t_0\le 2$ and special attention is given to the subclass $t_0=1$. Whereas there are no $\mathrm{\Lambda }$-term limits comprised in the class, the limit for vanishing vorticity leads to two previously derived irrotational dust families with $\mathrm{\Lambda }>0$, and the shear-free limit is the G"{o}del universe.