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.

arXiv commentv1: 27 pages + appendices; v2: typos fixed, conclusions added, matches published version in JHEP

References in corpus (46)

• Aspects of the BMS/CFT correspondence
• Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited
• BMS charge algebra
• Gravitational waveforms from inspiralling compact binaries to second-post-Newtonian order
• New Gravitational Memories
• The third post-Newtonian gravitational wave polarisations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits
• Conserved charges of the extended Bondi-Metzner-Sachs algebra
• New symmetries for the Gravitational S-matrix
• A 2D Stress Tensor for 4D Gravity
• Detecting gravitational-wave memory with LIGO: implications of GW150914
• Superboost transitions, refraction memory and super-Lorentz charge algebra
• The 2.5PN gravitational wave polarisations from inspiralling compact binaries in circular orbits
• Nonlinear gravitational-wave memory from binary black hole mergers
• The Weyl BMS group and Einstein's equations
• A perturbative and gauge invariant treatment of gravitational wave memory
• Searching for gravitational wave memory bursts with the Parkes Pulsar Timing Array
• Spin memory effect for compact binaries in the post-Newtonian approximation
• The Poincaré and BMS flux-balance laws with application to binary systems
• Computation of Displacement and Spin Gravitational Memory in Numerical Relativity
• New dual gravitational charges
• Center-of-mass angular momentum and memory effect in asymptotically flat spacetimes
• Quadrupole-quadrupole gravitational waves
• Persistent gravitational wave observables: general framework
• NANOGrav Constraints on Gravitational Wave Bursts with Memory
• Sub-subleading Soft Graviton Theorem from Asymptotic Einstein's Equations
• Gravity from symmetry: Duality and impulsive waves
• Fixing the BMS Frame of Numerical Relativity Waveforms
• BMS current algebra in the context of the Newman-Penrose formalism
• Gravitational Waves from Orphan Memory
• Tower of subleading dual BMS charges
• Multipole Expansion of Gravitational Waves: from Harmonic to Bondi coordinates
• Dual gravitational charges and soft theorems
• A note on the Newman-Unti group and the BMS charge algebra in terms of Newman-Penrose coefficients
• Gravitational multipole moments from Noether charges
• Gravitational breathing memory and dual symmetries
• Persistent gravitational wave observables: Curve deviation in asymptotically flat spacetimes
• Subleading BMS charges and fake news near null infinity
• Infinite towers of supertranslation and superrotation memories
• The Precession Caused by Gravitational Waves
• Flux-balance equations for linear momentum and center-of-mass position of self-gravitating post-Newtonian systems
• The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: From Source to Canonical Moment
• Metric reconstruction from celestial multipoles
• Radiation reaction in the 2.5PN waveform from inspiralling binaries in circular orbits
• The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: Relating the Harmonic and Radiative Metrics
• Gravitational memory effects and higher derivative actions
• Spin and Center of mass comparison between the PN approach and the asymptotic formulation

Cited by in corpus (15)

• Persistent gravitational wave observables: Curve deviation in asymptotically flat spacetimes
• Spin effects in gravitational waveforms and fluxes for binaries on eccentric orbits to the third post-Newtonian order
• The partial Bondi gauge: Gauge fixings and asymptotic charges
• Symmetries of the gravitational scattering in the absence of peeling
• Celestial $w_{1+\infty }$ charges and the subleading structure of asymptotically-flat spacetimes
• 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