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General Relativity and Quantum Cosmology, gr-qc
Abstract:
We compute the periastron advance using the effective-one-body formalism for
binary black holes moving on quasi-circular orbits and having spins collinear
with the orbital angular momentum. We compare the predictions with the
periastron advance recently computed in accurate numerical-relativity
simulations and find remarkable agreement for a wide range of spins and mass
ratios. These results do not use any numerical-relativity calibration of the
effective-one-body model, and stem from two key ingredients in the
effective-one-body Hamiltonian: (i) the mapping of the two-body dynamics of
spinning particles onto the dynamics of an effective spinning particle in a
(deformed) Kerr spacetime, fully symmetrized with respect to the two-body
masses and spins, and (ii) the resummation, in the test-particle limit, of all
post-Newtonian (PN) corrections linear in the spin of the particle. In fact,
even when only the leading spin PN corrections are included in the
effective-one-body spinning Hamiltonian but all the test-particle corrections
linear in the spin of the particle are resummed we find very good agreement
with the numerical results (within the numerical error for equal-mass binaries
and discrepancies of at most 1% for larger mass ratios). Furthermore, we
specialize to the extreme mass-ratio limit and derive, using the equations of
motion in the gravitational skeleton approach, analytical expressions for the
periastron advance, the meridional Lense-Thirring precession and spin
precession frequency in the case of a spinning particle on a nearly circular
equatorial orbit in Kerr spacetime, including also terms quadratic in the spin.
