Extended bodies with quadrupole moment interacting with gravitational monopoles: reciprocity relations

Details Extended bodies with quadrupole moment interacting with gravitational monopoles: reciprocity relations Extended bodies with quadrupole moment interacting with gravitational monopoles: reciprocity relations

2009-10-15

arxiv.org/abs/0910.2840v1

Gen.Rel.Grav.41:2781-2795,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, Latex svjour2.cls article class, 7 eps figure files. To appear on General Relativity and Gravitation, 2009

Scientific paper

10.1007/s10714-009-0807-9

An exact solution of Einstein's equations representing the static gravitational field of a quasi-spherical source endowed with both mass and mass quadrupole moment is considered. It belongs to the Weyl class of solutions and reduces to the Schwarzschild solution when the quadrupole moment vanishes. The geometric properties of timelike circular orbits (including geodesics) in this spacetime are investigated. Moreover, a comparison between geodesic motion in the spacetime of a quasi-spherical source and non-geodesic motion of an extended body also endowed with both mass and mass quadrupole moment as described by Dixon's model in the gravitational field of a Schwarzschild black hole is discussed. Certain "reciprocity relations" between the source and the particle parameters are obtained, providing a further argument in favor of the acceptability of Dixon's model for extended bodies in general relativity.

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