Gravitational-wave tail effects to quartic non-linear order

2016/07/31 by Tanguy Marchand, Luc Blanchet, Guillaume Faye
Physics and Astronomy · #Astrophysical Phenomena and Observations #Binary number #Cosmology and Gravitation Theories #Curvature #Gravitational wave #Limit (mathematics) #Order (exchange) #Perturbation (astronomy) #Pulsars and Gravitational Waves Research #Quadratic equation #Quartic function #gr-qc

paper · pdf · doi:10.1088/0264-9381/33/24/244003

published as Classical and Quantum Gravity, 2016, 33, 244003 · 32 pages, no figure, matches with published version

openalex created_date 2016/08/23 · openalex publication_date 2016/11/25 · arxiv created 2016/11/28 · arxiv updated 2016/12/07 · openalex updated_date 2026/08/05

Abstract

Gravitational-wave tails are due to the backscattering of linear waves onto the space-time curvature generated by the total mass of the matter source. The dominant tails correspond to quadratic non-linear interactions and arise at the one-and-a-half post-Newtonian (1.5 PN) order in the gravitational waveform. The 'tails-of-tails', which are cubic non-linear effects appearing at the 3 PN order in the waveform, are also known. We derive here higher non-linear tail effects, namely those associated with quartic non-linear interactions or 'tails-of-tails-of-tails', which are shown to arise at the 4.5 PN order. As an application, we obtain at that order the complete coefficient in the total gravitational-wave energy flux of compact binary systems moving on circular orbits. Our result perfectly agrees with black-hole perturbation calculations in the limit of extreme mass ratio of the two compact objects.

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