Reconstructing the Gravitational Waveform from Its Probe Limit

TL;DR

This paper demonstrates how to reconstruct full gravitational waveforms for binary systems from their probe limit by leveraging polynomial mass dependence and symmetry, simplifying high-order post-Newtonian calculations.

Contribution

It introduces a method to derive generic mass waveforms from probe limit results using polynomial properties and symmetry, advancing waveform modeling in gravitational wave physics.

Findings

Reconstructed waveforms up to 5PN for generic masses.

Calculated probe-limit waveforms up to 10PN in the small-velocity regime.

Simplified the PN expansion of subleading PM waveforms.

Abstract

Gravitational observables for binary systems exhibit a simple polynomial dependence on the masses $m_1$, $m_2$ of the two scattering objects when they are written in terms of the appropriate kinematic variables in the post-Minkowskian (PM) regime. We point out that this property, combined with particle interchange symmetry, allows one to reconstruct the leading and subleading PM waveforms from their probe limit, $m_1 \gg m_2$. As an application, focusing on their re-expansion in the small-velocity or post-Newtonian (PN) regime, we calculate the probe-limit waveforms up to 10PN, and then exploit this observation to deduce from them the waveforms for generic masses in the center-of-mass frame up to 5PN. To this end, we employ both the amplitude-based waveform integrands and the tail formula. This combined approach simplifies substantially the PN expansion of the full subleading PM waveform.