General static axisymmetric solution of Einstein's vacuum field equations in prolate spheroidal coordinates

Details General static axisymmetric solution of Einstein's vacuum field equations in prolate spheroidal coordinates General static axisymmetric solution of Einstein's vacuum field equations in prolate spheroidal coordinates

May 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989phrvd..39.2904q&link_type=abstract

Physical Review D (Particles and Fields), Volume 39, Issue 10, 15 May 1989, pp.2904-2911

Physics

49

Exact Solutions, Celestial Mechanics

Scientific paper

A solution of Einstein's vacuum field equations is presented explicitly in Eqs. (22), (28), and (43). This completes our stationary metric presented previously and therefore gives the exact solution to the problem of describing the exterior field of rotating deformed bodies. The metric given here is equivalent to the general Weyl metric; however, we use prolate spheroidal coordinates for conve- nience. We investigate the Newtonian and the relativistic (Geroch-Hansen) multipole moments of the solution and conclude that it describes the exterior gravitational field of a static axisymmetric mass distribution.

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