# Energetics of two-body Hamiltonians in post-Minkowskian gravity

## TL;DR

This paper evaluates the effectiveness of post-Minkowskian (PM) approximations in modeling binary inspiral dynamics by comparing them with numerical relativity results, highlighting the need for higher-order PM calculations for improved gravitational wave predictions.

## Contribution

It provides a quantitative comparison of PM, EOB, and PN models against numerical relativity for binary systems, emphasizing the importance of higher-order PM results for gravitational wave modeling.

## Key findings

- 3PM results improve agreement with NR over 2PM.
- Higher-order PM calculations are necessary for better waveform models.
- PM models are promising but require further refinement for LIGO/Virgo accuracy.

## Abstract

Advanced methods for computing perturbative, quantum-gravitational scattering amplitudes show great promise for improving our knowledge of classical gravitational dynamics. This is especially true in the weak-field and arbitrary-speed (post-Minkowskian, PM) regime, where the conservative dynamics at 3PM order has been recently determined for the first time, via an amplitude calculation. Such PM results are most relevantly applicable to relativistic scattering (unbound orbits), while bound/inspiraling binary systems, the most frequent sources of gravitational waves for the LIGO and Virgo detectors, are most suitably modeled by the weak-field and slow-motion (post-Newtonian, PN) approximation. Nonetheless, it has been suggested that PM results can independently lead to improved modeling of bound binary dynamics, especially when taken as inputs for effective-one-body (EOB) models of inspiraling binaries. Here, we initiate a quantitative study of this possibility, by comparing PM, EOB and PN predictions for the binding energy of a two-body system on a quasi-circular inspiraling orbit against results of numerical relativity (NR) simulations. The binding energy is one of the two central ingredients (the other being the gravitational-wave energy flux) that enters the computation of gravitational waveforms employed by LIGO and Virgo detectors, and for (quasi-)circular orbits it provides an accurate diagnostic of the conservative sector of a model. We find that, whereas 3PM results do improve the agreement with NR with respect to 2PM (especially when used in the EOB framework), it is crucial to push PM calculations at higher orders if one wants to achieve better performances than current waveform models used for LIGO/Virgo data analysis.