Quadrupole effects on the motion of extended bodies in Kerr spacetime

Abstract

The motion of a body endowed with dipolar as well as quadrupolar structure is investigated in the Kerr background according to the Dixon's model, extending a previous analysis done in the Schwarzschild background. The full set of evolution equations is solved under the simplifying assumptions of constant frame components for both the spin and the quadrupole tensors and that the center of mass moves along an equatorial circular orbit, the total four-momentum of the body being aligned with it. We find that the motion deviates from the geodesic one due to the internal structure of the body, leading to measurable effects. Corrections to the geodesic value of the orbital period of a close binary system orbiting the Galactic Center are discussed assuming that the Galactic Center is a Kerr supermassive black hole.

arXiv comment9 pages, latex iopart class document, no figures. Note that the second term in the rhs of Eq. (1.2) was misprinted in the published version of the paper [Classical and Quantum Gravity, Vol. 25, 125007 (2008)]. The results are but correct

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• Highly relativistic circular orbits of spinning particle in the Kerr field
• Self-forces from generalized Killing fields
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• Dynamics of quadrupolar bodies in a Schwarzschild spacetime
• Highly relativistic spinning particle in the Schwarzschild field: Circular and other orbits
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• Detweiler's redshift invariant for extended bodies orbiting a Schwarzschild black hole
• Motion of pole-dipole and quadrupole particles in non-minimally coupled theories of gravity
• Extended bodies moving on geodesic trajectories
• Spin dynamics of moving bodies in rotating black hole spacetimes
• Extended bodies with quadrupole moment interacting with gravitational monopoles: reciprocity relations
• Precisely computing bound orbits of spinning bodies around black holes I: General framework and results for nearly equatorial orbits