# Comparison of post-Newtonian mode amplitudes with numerical relativity simulations of binary black holes

## TL;DR

This study compares post-Newtonian and numerical relativity waveforms from binary black hole mergers, finding good agreement in many modes even during highly dynamical phases, which aids in improving gravitational waveform models.

## Contribution

It demonstrates that leading order post-Newtonian amplitudes closely match numerical relativity results for many modes during strong-field black hole mergers.

## Key findings

- Post-Newtonian amplitudes agree well with numerical relativity for many modes.
- Modes with l = m and l = 2, m = 1 are least modified from post-Newtonian predictions.
- Understanding these modes helps improve models of gravitational waveforms in strong gravity regimes.

## Abstract

Gravitational waves from the coalescence of two black holes carry the signature of the strong field dynamics of binary black holes. In this work we have used numerical relativity simulations and post-Newtonian theory to investigate this dynamics. Post-Newtonian theory is a low-velocity expansion that assumes the companion bodies to be point-particles, while numerical relativity treats black holes as extended objects with horizons and fully captures their dynamics. There is a priori no reason for the waveforms computed using these disparate methods to agree with each other, especially at late times when the black holes move close to the speed of light. We find, remarkably, that the leading order amplitudes in post-Newtonian theory agree well with the full general relativity solution for a large set of spherical harmonic modes, even in the most dynamical part of the binary evolution, with only some modes showing distinctly different behavior than that found by numerical relativity simulations. In particular, modes with spherical harmonic indices l = m as well as l = 2, m = 1 are least modified from their dominant post-Newtonian behavior. Understanding the nature of these modes in terms of the post-Newtonian description will aid in formulating better models of the emitted waveforms in the strong field regime of the dynamics.