Abstract
The stationary and axially symmetric gravitational field due to a rotating deformed source can be treated by the Ernst equation. We prove analytically the validity of the solution of the Ernst equation that was presented as a possible solution in a previous paper for arbitrary real values of the deformation parameter δ. By means of analytic continuations of the solution we obtain a new solution in oblate spheroidal coordinates. This leads to a metric different from the Tomimatsu-Sato metric. From these solutions for real δ we determine the metric functions both in prolate and oblate spheroidal coordinates.
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