The current-type quadrupole moment and gravitational-wave mode $(\ell ,m)=(2,1)$ of compact binary systems at the third post-Newtonian order

Abstract

Up to the third post-Newtonian (3PN) order, we compute (i) the current-type quadrupole moment of (non-spinning) compact binary systems, as well as (ii) the corresponding gravitational-wave mode $(2,1)$ (constituting a 3.5PN correction in the waveform). Moreover, at this occasion, (iii) we recompute and confirm the previous calculation of the mass-type octupole moment to 3PN order. The ultra-violet (UV) divergences due to the point-like nature of the source are treated by means of dimensional regularization. This entails generalizing the definition of the irreducible mass and current multipole moments of an isolated PN source in $d$ spatial dimensions. In particular, we find that the current type moment has the symmetry of a particular mixed Young tableau and that, in addition, there appears a third type of moment which is however inexistent in 3 spatial dimensions.

24 pages

References in corpus (7)

• Using Full Information When Computing Modes of Post-Newtonian Waveforms From Inspiralling Compact Binaries in Circular Orbit
• The third and a half post-Newtonian gravitational wave quadrupole mode for quasi-circular inspiralling compact binaries
• Cubic order spin effects in the dynamics and gravitational wave energy flux of compact object binaries
• Gravitational-wave observations of binary black holes: Effect of non-quadrupole modes
• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: potential contributions
• Non-linear multipole interactions and gravitational-wave octupole modes for inspiralling compact binaries to third-and-a-half post-Newtonian order
• High-order half-integral conservative post-Newtonian coefficients in the redshift factor of black hole binaries

Cited by in corpus (29)

• 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 waves in scalar-tensor theory to one-and-a-half post-Newtonian order
• Gravitational radiation from inspiralling compact objects: Spin effects to fourth Post-Newtonian order
• Gravitational Wave Flux and Quadrupole Modes from Quasi-Circular Non-Spinning Compact Binaries to the Fourth Post-Newtonian Order
• Radiated momentum and radiation-reaction in gravitational two-body scattering including time-asymmetric effects
• Spin effects in gravitational waveforms and fluxes for binaries on eccentric orbits to the third post-Newtonian order
• Spin contributions to the gravitational-waveform modes for spin-aligned binaries at the 3.5PN order
• High accuracy post-Newtonian and numerical relativity comparisons involving higher modes for eccentric binary black holes and a dominant mode eccentric inspiral-merger-ringdown model
• Gravitational-wave tails of memory
• The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: From Source to Canonical Moment
• Complete gravitational-waveform amplitude modes for quasi-circular compact binaries to the 3.5PN order
• ESIGMAHM: An Eccentric, Spinning inspiral-merger-ringdown waveform model with Higher Modes for the detection and characterization of binary black holes
• 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
• Multipole expansion at the level of the action in $d$-dimensions
• Conservative (failed)-tail effects at the fifth post-Newtonian order
• 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 from inspiralling compact binaries to N${}^3$LO in the Effective Field Theory approach
• Schott term in the binding energy for compact binaries on circular orbits at fourth post-Newtonian order
• Tidal contributions to the full gravitational waveform to the second-and-a-half post-Newtonian order
• Post-Newtonian Dynamics of Spinning Black Hole Binaries in Einstein-Scalar-Gauss-Bonnet 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
• Tidal effects in the total flux and waveform in massless scalar-tensor theories to, respectively, relative 2PN and 1.5PN orders