Post-Newtonian theory for gravitational waves

Abstract To be observed and analyzed by the network of current gravitational-wave detectors (LIGO, Virgo, KAGRA), and in anticipation of future third generation ground-based (Einstein Telescope, Cosmic Explorer) and space-borne (LISA) detectors, inspiralling compact binaries—binary star systems comp...

Full description

Saved in:
Bibliographic Details
Main Author: Luc Blanchet
Format: Article
Language:English
Published: SpringerOpen 2024-07-01
Series:Living Reviews in Relativity
Subjects:
Online Access:https://doi.org/10.1007/s41114-024-00050-z
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850102924883001344
author Luc Blanchet
author_facet Luc Blanchet
author_sort Luc Blanchet
collection DOAJ
description Abstract To be observed and analyzed by the network of current gravitational-wave detectors (LIGO, Virgo, KAGRA), and in anticipation of future third generation ground-based (Einstein Telescope, Cosmic Explorer) and space-borne (LISA) detectors, inspiralling compact binaries—binary star systems composed of neutron stars and/or black holes in their late stage of evolution prior the final coalescence—require high-accuracy predictions from general relativity. The orbital dynamics and emitted gravitational waves of these very relativistic systems can be accurately modelled using state-of-the-art post-Newtonian theory. In this article we review the multipolar-post-Minkowskian approximation scheme, merged to the standard post-Newtonian expansion into a single formalism valid for general isolated matter system. This cocktail of approximation methods (called MPM-PN) has been successfully applied to compact binary systems, producing equations of motion up to the fourth-post-Newtonian (4PN) level, and gravitational waveform and flux to 4.5PN order beyond the Einstein quadrupole formula. We describe the dimensional regularization at work in such high post-Newtonian calculations, for curing both ultra-violet and infra-red divergences. Several landmark results are detailed: the definition of multipole moments, the gravitational radiation reaction, the conservative dynamics of circular orbits, the first law of compact binary mechanics, and the non-linear effects in the gravitational-wave propagation (tails, iterated tails and non-linear memory). We also discuss the case of compact binaries moving on eccentric orbits, and the effects of spins (both spin-orbit and spin–spin) on the equations of motion and gravitational-wave energy flux and waveform.
format Article
id doaj-art-871fefb2b54a4708ba022e19224bc5fc
institution DOAJ
issn 1433-8351
language English
publishDate 2024-07-01
publisher SpringerOpen
record_format Article
series Living Reviews in Relativity
spelling doaj-art-871fefb2b54a4708ba022e19224bc5fc2025-08-20T02:39:39ZengSpringerOpenLiving Reviews in Relativity1433-83512024-07-01271129210.1007/s41114-024-00050-zPost-Newtonian theory for gravitational wavesLuc Blanchet0Institut d’Astrophysique de ParisAbstract To be observed and analyzed by the network of current gravitational-wave detectors (LIGO, Virgo, KAGRA), and in anticipation of future third generation ground-based (Einstein Telescope, Cosmic Explorer) and space-borne (LISA) detectors, inspiralling compact binaries—binary star systems composed of neutron stars and/or black holes in their late stage of evolution prior the final coalescence—require high-accuracy predictions from general relativity. The orbital dynamics and emitted gravitational waves of these very relativistic systems can be accurately modelled using state-of-the-art post-Newtonian theory. In this article we review the multipolar-post-Minkowskian approximation scheme, merged to the standard post-Newtonian expansion into a single formalism valid for general isolated matter system. This cocktail of approximation methods (called MPM-PN) has been successfully applied to compact binary systems, producing equations of motion up to the fourth-post-Newtonian (4PN) level, and gravitational waveform and flux to 4.5PN order beyond the Einstein quadrupole formula. We describe the dimensional regularization at work in such high post-Newtonian calculations, for curing both ultra-violet and infra-red divergences. Several landmark results are detailed: the definition of multipole moments, the gravitational radiation reaction, the conservative dynamics of circular orbits, the first law of compact binary mechanics, and the non-linear effects in the gravitational-wave propagation (tails, iterated tails and non-linear memory). We also discuss the case of compact binaries moving on eccentric orbits, and the effects of spins (both spin-orbit and spin–spin) on the equations of motion and gravitational-wave energy flux and waveform.https://doi.org/10.1007/s41114-024-00050-zGravitational radiationPost-Newtonian approximationPost-Minkowskian approximationMultipolar expansionDimensional regularizationEquations of motion
spellingShingle Luc Blanchet
Post-Newtonian theory for gravitational waves
Living Reviews in Relativity
Gravitational radiation
Post-Newtonian approximation
Post-Minkowskian approximation
Multipolar expansion
Dimensional regularization
Equations of motion
title Post-Newtonian theory for gravitational waves
title_full Post-Newtonian theory for gravitational waves
title_fullStr Post-Newtonian theory for gravitational waves
title_full_unstemmed Post-Newtonian theory for gravitational waves
title_short Post-Newtonian theory for gravitational waves
title_sort post newtonian theory for gravitational waves
topic Gravitational radiation
Post-Newtonian approximation
Post-Minkowskian approximation
Multipolar expansion
Dimensional regularization
Equations of motion
url https://doi.org/10.1007/s41114-024-00050-z
work_keys_str_mv AT lucblanchet postnewtoniantheoryforgravitationalwaves