Periastron Advance in Spinning Black Hole Binaries: Gravitational Self-Force from Numerical Relativity

TL;DR

This paper combines numerical relativity, post-Newtonian approximation, and black hole perturbation theory to accurately measure the gravitational self-force effect on periastron advance in spinning black hole binaries, improving theoretical predictions.

Contribution

It introduces an improved perturbative expansion based on symmetry considerations, enabling precise measurement of self-force effects in spinning black hole binaries.

Findings

Excellent agreement between perturbative expansion and numerical relativity results.

First measurement of self-force effects on periastron advance in Kerr black hole orbits.

Validation of the new expansion method across various spins and separations.

Abstract

We study the general relativistic periastron advance in spinning black hole binaries on quasi-circular orbits, with spins aligned or anti-aligned 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 non-spinning particle orbiting a Kerr black hole of mass M and spin S = -0.5 M^2, 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.