Comparison of Post-Newtonian and Numerical Evolutions of Black-Hole Binaries

TL;DR

This study compares post-Newtonian waveforms with numerical simulations of generic black-hole binaries, showing high agreement in the early inspiral phase for various modes, validating the PN approach for certain regimes.

Contribution

It provides a detailed comparison between PN and numerical waveforms for generic black-hole binaries with specific mass ratios and spins, highlighting their agreement.

Findings

Over 98% waveform overlap for the first six cycles of dominant modes

Over 90% overlap for subdominant modes

Good agreement validates PN methods for early inspiral phase

Abstract

In this paper, we compare the waveforms from the post-Newtonian (PN) approach with the numerical simulations of generic black-hole binaries which have mass ratio $q\sim0.8$, arbitrarily oriented spins with magnitudes $S_1/m_1^2\sim0.6$ and $S_2/m_2^2\sim0.4$, and orbit 9 times from an initial orbital separation of $r\approx11M$ prior to merger. We observe a reasonably good agreement between the PN and numerical waveforms, with an overlap of over 98% for the first six cycles of the $(\ell=2,m=\pm2)$ mode and over 90% for the $(\ell=2,m=1)$ and $(\ell=3,m=3)$ modes.