Periastron advance in spinning black hole binaries: comparing effective-one-body and Numerical Relativity

TL;DR

This study compares effective-one-body predictions with numerical relativity simulations for periastron advance in spinning black hole binaries, showing excellent agreement across various spins and mass ratios without calibration.

Contribution

It demonstrates that the effective-one-body formalism accurately predicts periastron advance in spinning black hole binaries without requiring numerical-relativity calibration.

Findings

Remarkable agreement between EOB and numerical relativity for a wide range of parameters.

EOB model's key ingredients include a symmetrized mapping and resummation of spin corrections.

Analytical expressions derived for extreme mass-ratio limit with spin effects.

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.