Gravitational waves from inspiralling compact binaries: Energy flux to third post-Newtonian order

TL;DR

The paper develops a complete 3PN calculation of the gravitational-wave energy flux from inspiralling compact binaries using the multipolar-post-Minkowskian framework and Hadamard regularization, including tails up to 3.5PN. It derives the source multipole moments, notably the mass quadrupole at 3PN, and the current quadrupole and mass octupole at 2PN, and then connects these to radiative moments to obtain the luminosity. A key finding is that Hadamard regularization introduces ambiguities (captured by a parameter θ, and via λ from the equations of motion) that collapse into a single physical combination in the flux for circular orbits, λ − (2/3)θ, leaving one undetermined degree of freedom. The results are cross-checked against black-hole perturbation theory in the test-mass limit, and the formalism provides a basis for high-precision gravitational-wave templates, including the tail and tail-of-tail non-linear effects essential for accurate waveform modeling.

Abstract

The multipolar-post-Minkowskian approach to gravitational radiation is applied to the problem of the generation of waves by the compact binary inspiral. We investigate specifically the third post-Newtonian (3PN) approximation in the total energy flux. The new results are the computation of the mass quadrupole moment of the binary to the 3PN order, and the current quadrupole and mass octupole to the 2PN order. Wave tails and tails of tails in the far zone are included up to the 3.5PN order. The recently derived 3PN equations of binary motion are used to compute the time-derivatives of the moments. We find perfect agreement to the 3.5PN order with perturbation calculations of black holes in the test-mass limit for one body. Technical inputs in our computation include a model of point particles for describing the compact objects, and the Hadamard self-field regularization. Because of a physical incompleteness of the Hadamard regularization at the 3PN order, the energy flux depends on one unknown physical parameter, which is a combination of a parameter λin the equations of motion, and a new parameter θcoming from the quadrupole moment.