The gravitational field of rotating bodies

Details The gravitational field of rotating bodies The gravitational field of rotating bodies

Nov 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991zhetf.100.1423p&link_type=abstract

Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki (ISSN 0044-4510), vol. 100, Nov. 1991, p. 1423-1437. In Russian.

Mathematics

Einstein Equations, Gravitational Fields, Relativity, Rotating Bodies, Oblate Spheroids, Prolate Spheroids, Singularity (Mathematics)

Scientific paper

Two vacuum solutions for the Einstein equations are obtained and analyzed, which can be regarded as candidates for the role of an external solution for the axisymmetric steadily rotating bodies, both prolate and oblate, respectively. Both solutions contain two infinite sets of arbitrary constants corresponding to the multipoles of the mass and angular momentum. It is shown that, in the absence of rotation and with a definite choice of the mass multipole moments, the first solution goes over into the Zipoy (1966) and Voorhees (1970) metric while the second solution goes over into the known solution with ring singularity. The relationship between the first solution and the Van Stockum (1937) metric is analyzed, clarifying the interpretation of the latter.

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