Reconstructing the Gravitational Waveform from Its Probe Limit
Carlo Heissenberg, Rodolfo Russo
TL;DR
This work shows that the gravitational waveform in the post-Minkowskian regime can be fully reconstructed from its probe-limit data at leading and subleading orders by exploiting polynomial mass dependence and particle interchange symmetry. The authors develop a Lorentz-boost based reconstruction pipeline that connects rest-frame probe results to the center-of-mass frame, and apply it to obtain leading and subleading PM waveforms up to rest-frame $10$PN and CM $5$PN, including a detailed treatment of Compton cuts and the tail formula. They decompose the waveform into TT components using the $\xi_{\pm}^{\mu\nu}$ basis, and demonstrate how, together with the amplitude-based approach and symmetry, the full radiative observables can be obtained from the probe limit, with cross-checks against known results for energy and angular-momentum flux. The approach clarifies the link between PM radiative observables and self-force/amplitude-based methods, offering a practical route to higher-order PN expansions for binaries.
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.