The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: From Source to Canonical Moment

Abstract

As a crucial step towards the completion of the fourth post-Newtonian (4PN) gravitational-wave generation from compact binary systems, we obtain the expressions of the so-called "canonical" multipole moments of the source in terms of the "source" and "gauge" moments. The canonical moments describe the propagation of gravitational waves outside the source's near zone, while the source and gauge moments encode explicit information about the matter source. Those two descriptions, in terms of two sets of canonical moments or in terms of six sets of source and gauge moments, are isometric. We thus construct the non-linear diffeomorphism between them up to the third post-Minkowskian order, and we exhibit the concrete expression of the canonical mass-type quadrupole moment at the 4PN order. This computation is one of the last missing pieces for the determination of the gravitational-wave phasing of compact binary systems at 4PN order.

25 pages, no figure

References in corpus (7)

• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• Advanced LIGO
• The third and a half post-Newtonian gravitational wave quadrupole mode for quasi-circular inspiralling compact binaries
• Non-linear multipole interactions and gravitational-wave octupole modes for inspiralling compact binaries to third-and-a-half post-Newtonian order
• The current-type quadrupole moment and gravitational-wave mode $(\ell ,m)=(2,1)$ of compact binary systems at the third post-Newtonian order
• 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: II. Dimensional Regularization and Renormalization

Cited by in corpus (19)

• The Science of the Einstein Telescope
• Gravitational-Wave Phasing of Quasi-Circular Compact Binary Systems to the Fourth-and-a-Half post-Newtonian Order
• Gravitational Wave Flux and Quadrupole Modes from Quasi-Circular Non-Spinning Compact Binaries to the Fourth Post-Newtonian Order
• Spin contributions to the gravitational-waveform modes for spin-aligned binaries at the 3.5PN order
• Gravitational-wave tails of memory
• Complete gravitational-waveform amplitude modes for quasi-circular compact binaries to the 3.5PN order
• Multipole expansion of gravitational waves: memory effects and Bondi aspects
• The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: Relating the Harmonic and Radiative Metrics
• Quasi-Keplerian parametrization for eccentric compact binaries in scalar-tensor theories at second post-Newtonian order and applications
• Gravitational memory: new results from post-Newtonian and self-force theory
• Electromagnetic fields in compact binaries: post-Newtonian wave generation and application to double white dwarfs systems
• Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order
• Schott term in the binding energy for compact binaries on circular orbits at fourth post-Newtonian order
• Gravitational Radiation from Eccentric Binary Black Hole System in Dynamical Chern-Simons Gravity
• Parametrized multipolar gravitational waveforms for testing general relativity: Amplitude corrections up to 2PN order
• Tests of general relativity at the fourth post-Newtonian order
• Comparison of 4.5PN and 2SF gravitational energy fluxes from quasicircular compact binaries
• Approximate helical symmetry in compact binaries
• Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order in harmonic coordinates