Energy versus Angular Momentum in Black Hole Binaries

TL;DR

This paper uses numerical relativity simulations to analyze the energy-angular momentum relation in nonspinning black-hole binaries, demonstrating the effectiveness of the effective one-body formalism over traditional post-Newtonian methods.

Contribution

It provides the first detailed comparison of numerical relativity results with analytical models for the energy-angular momentum relation in black-hole binaries, highlighting the accuracy of the effective one-body approach.

Findings

The $E(j)$ relation accurately reflects the binary dynamics.

Post-Newtonian $E(j)$ deviates significantly from numerical results.

Effective one-body formalism matches numerical relativity predictions closely.

Abstract

Using accurate numerical relativity simulations of (nonspinning) black-hole binaries with mass ratios 1:1, 2:1 and 3:1 we compute the gauge invariant relation between the (reduced) binding energy $E$ and the (reduced) angular momentum $j$ of the system. We show that the relation $E(j)$ is an accurate diagnostic of the dynamics of a black-hole binary in a highly relativistic regime. By comparing the numerical-relativity $E^{\rm NR} (j)$ curve with the predictions of several analytic approximation schemes, we find that, while the usual, non-resummed post-Newtonian-expanded $E^{\rm PN} (j)$ relation exhibits large and growing deviations from $E^{\rm NR} (j)$, the prediction of the effective one-body formalism, based purely on known analytical results (without any calibration to numerical relativity), agrees strikingly well with the numerical-relativity results.