Limits of the generalised Tomimatsu-Sato gravitational fields

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Abstract
The author has previously presented a new three-parameter family of exact asymptotically flat stationary axisymmetric vacuum solutions of Einstein's equations which contains the solutions of Kerr and Tomimatsu-Sato (TS) as special cases. In this paper, he considers two special cases of the previous family which must be constructed by a limiting process. These are interpreted as a 'rotating Curzon metric' and a 'generalised extreme Kerr metric'. In addition, approximate forms for the original metrics are given for the case of slow rotation and small deformation.