Gravitational Self-Force Correction to the Binding Energy of Compact Binary Systems

TL;DR

This paper uses the first law of binary black-hole mechanics to compute the binding energy and angular momentum of non-spinning compact binaries, confirming the validity of perturbative methods beyond extreme mass ratios.

Contribution

It introduces a method to calculate the binding energy and angular momentum including gravitational self-force effects, extending perturbative results to comparable-mass binaries.

Findings

Accurately recovers the ISCO frequency shift due to self-force.

Shows strong agreement with numerical simulations in the strong-field regime.

Extends the applicability of perturbative calculations beyond extreme mass ratios.

Abstract

Using the first law of binary black-hole mechanics, we compute the binding energy E and total angular momentum J of two non-spinning compact objects moving on circular orbits with frequency Omega, at leading order beyond the test-particle approximation. By minimizing E(Omega) we recover the exact frequency shift of the Schwarzschild innermost stable circular orbit induced by the conservative piece of the gravitational self-force. Comparing our results for the coordinate invariant relation E(J) to those recently obtained from numerical simulations of comparable-mass non-spinning black-hole binaries, we find a remarkably good agreement, even in the strong-field regime. Our findings confirm that the domain of validity of perturbative calculations may extend well beyond the extreme mass-ratio limit.