Multipole expansion of gravitational waves: memory effects and Bondi aspects

TL;DR

This work extends the multipolar post-Minkowskian formalism by deriving the Newman-Unti metric and Bondi data for quadratic interactions between mass quadrupoles, including both instantaneous and hereditary terms. It confirms the displacement memory within NU/Lorentz frameworks, computes full NU metric components for monopole-quadrupole and quadrupole-quadrupole couplings, and translates these to Bondi data while elucidating memory, tails, and mass-loss effects. The authors also analyze gravitational charges, establishing Newman-Penrose charge conservation in this sector and detailing the dressed Bondi aspects and celestial charges up to order three. The results deepen the connection between PN/MPM formalisms and radiative asymptotic structures, with explicit expressions for NP, BMS, and celestial charges that can inform future waveform modeling and observational probes of memory effects.

Abstract

In our previous work, we proposed an algorithm to transform the metric of an isolated matter source in the multipolar post-Minkowskian approximation in harmonic (de Donder) gauge to the Newman-Unti gauge. We then applied this algorithm at linear order and for specific quadratic interactions known as quadratic tail terms. In the present work, we extend this analysis to quadratic interactions associated with the coupling of two mass quadrupole moments, including both instantaneous and hereditary terms. Our main result is the derivation of the metric in Newman-Unti and Bondi gauges with complete quadrupole-quadrupole interactions. We rederive the displacement memory effect and provide expressions for all Bondi aspects and dressed Bondi aspects relevant to the study of leading and subleading memory effects. Then we obtain the Newman-Penrose charges, the BMS charges as well as the second and third order celestial charges defined from the known second order and novel third order dressed Bondi aspects for mass monopole-quadrupole and quadrupole-quadrupole interactions.