Extended bodies with quadrupole moment interacting with gravitational monopoles: reciprocity relations |
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| Authors: | Donato Bini Christian Cherubini Simonetta Filippi and Andrea Geralico |
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| Institution: | 1.Istituto per le Applicazioni del Calcolo “M. Picone”, CNR,Rome,Italy;2.ICRA, University of Rome “La Sapienza”,Rome,Italy;3.INFN, Sezione di Firenze, Polo Scientifico,Sesto Fiorentino (FI),Italy;4.Nonlinear Physics and Mathematical Modeling Lab, Engineering Faculty,University Campus Bio-Medico,Rome,Italy;5.Physics Department and ICRA,University of Rome “La Sapienza”,Rome,Italy |
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| Abstract: | 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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