Periastron advance in spinning black hole binaries: Gravitational self-force from numerical relativity

We study the general relativistic periastron advance in spinning black hole binaries on quasicircular orbits, with spins aligned or antialigned with the orbital angular momentum, using numerical-relativity simulations, the post-Newtonian approximation, and black hole perturbation theory. By imposing a symmetry by exchange of the bodies' labels, we devise an improved version of the perturbative result and use it as the leading term of a new type of expansion in powers of the symmetric mass ratio. This allows us to measure, for the first time, the gravitational self-force effect on the periastron advance of a nonspinning particle orbiting a Kerr black hole of mass M and spin S=-0.5M², down to separations of order $9M$. Comparing the predictions of our improved perturbative expansion with the exact results from numerical simulations of equal-mass and equal-spin binaries, we find a remarkable agreement over a wide range of spins and orbital separations.