A Solution of the Einstein Equation in a Stationary Gravitational Field Due to a Rotating Source

Details A Solution of the Einstein Equation in a Stationary Gravitational Field Due to a Rotating Source A Solution of the Einstein Equation in a Stationary Gravitational Field Due to a Rotating Source

Feb 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999pthph.101..329t&link_type=abstract

Progress of Theoretical Physics, Vol. 101, No. 2, pp. 329-344.

Physics

2

Scientific paper

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 &delta. 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 &delta we determine the metric functions both in prolate and oblate spheroidal coordinates.

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