Influence of internal structure on the motion of test bodies in extreme mass ratio situations

Abstract

We investigate the motion of test bodies with internal structure in General Relativity. With the help of a multipolar approximation method for extended test bodies we derive the equations of motion up to the quadrupolar order. The motion of pole-dipole and quadrupole test bodies is studied in the context of the Kerr geometry. For an explicit quadrupole model, which includes spin and tidal interactions, the motion in the equatorial plane is characterized by an effective potential and by the binding energy. We compare our findings to recent results for the conservative part of the self-force of bodies in extreme mass ratio situations. Possible implications for gravitational wave physics are outlined.

23 pages, 6 figures, RevTex format

References in corpus (17)

• Relativistic theory of tidal Love numbers
• Higher-order spin effects in the dynamics of compact binaries I. Equations of motion
• xPerm: fast index canonicalization for tensor computer algebra
• Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling
• Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole
• Osculating orbits in Schwarzschild spacetime, with an application to extreme mass-ratio inspirals
• Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach
• ADM canonical formalism for gravitating spinning objects
• Higher-order-in-spin interaction Hamiltonians for binary black holes from Poincaré invariance
• Canonical Formulation of Spin in General Relativity
• Reduced Hamiltonian for next-to-leading order Spin-Squared Dynamics of General Compact Binaries
• Second-order gravitational self-force
• Dynamics of test bodies with spin in de Sitter spacetime
• Comment on recent papers regarding next-to-leading order spin-spin effects in gravitational interaction
• Quadrupole effects on the motion of extended bodies in Kerr spacetime
• Quadrupole effects on the motion of extended bodies in Schwarzschild spacetime
• Extended-body effects in cosmological spacetimes

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• Actions of spinning compact binaries: Spinning particle in Kerr matched to dynamics at 1.5 post-Newtonian order
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