Limits of the Tomimatsu-Sato gravitational field

The Tomimatsu-Sato (TS) solutions of the Einstein field equations are studied in several limiting cases. In the weak-field limit we construct two Newtonian models for the source, one consisting of a rotating disc of radius a/n, the other made up of n complex point multipoles. The "extreme" limit q = 1 is also examined in detail, and we find there are many distinct ways of taking this limit. We are thereby led to a new two-parameter family of exact solutions which, unlike the TS metrics, are not asymptotically flat.