I. Racz et M. Suveges, ON THE UNIQUENESS OF STATIONARY AXISYMMETRICAL ELLIPSOIDAL VACUUM CONFIGURATIONS, Modern physics letters A, 13(14), 1998, pp. 1101-1107
Stationary axisymmetric vacuum space-times in general relativity are c
onsidered. The Riemannian metric induced on the space of the time-like
Killing trajectories is assumed to be ellipsoidal. It is demonstrated
that the only ellipsoidal solutions of the vacuum Einstein's equation
s are the Kerr-NUT family with vanishing electric and magnetic charges
.