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...
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SpringerOpen
2024-07-01
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| Series: | Living Reviews in Relativity |
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| Online Access: | https://doi.org/10.1007/s41114-024-00050-z |
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| 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 |