Multipole expansion of gravitational waves: memory effects and Bondi aspects

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.

v1: 27 pages + appendices; v2: typos fixed, conclusions added, matches published version in JHEP

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• Gravitational memory: new results from post-Newtonian and self-force theory
• Higher memory effects and the post-Newtonian calculation of their gravitational-wave signals
• Electromagnetic fields in compact binaries: post-Newtonian wave generation and application to double white dwarfs systems
• Gyroscopic Gravitational Memory from quasi-circular binary systems
• On the covariant formulation of gauge theories with boundaries
• Celestial $s{w}_{1+\infty }$ algebra in Einstein-Yang-Mills theory
• Gravitational wave pulse and memory effects for hairy Kiselev black hole and its analogy with Bondi-Sachs formalism
• Gravitational memory effects of black bounces and a traversable wormhole
• Note on post-Minkowskian expansion and Bondi coordinates
• Gravitational memory meets astrophysical environments: exploring a new frontier through osculations