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Comptes Rendus Physique
Sous presse. Epreuves corrigées par l'auteur. Disponible en ligne depuis le vendredi 8 mars 2019
Doi : 10.1016/j.crhy.2019.02.004
Analyzing gravitational waves with general relativity
Analyser les ondes gravitationnelles avec la relativité générale
 

Luc Blanchet
 Institut d'astrophysique de Paris, UMR 7095, CNRS, Sorbonne Université, 98bis, boulevard Arago, 75014 Paris, France 

Abstract

After a short review of prominent properties of gravitational waves and of the newly born gravitational astronomy, we focus on theoretical aspects. Analytic approximation methods in general relativity have played a crucial role in the recent discoveries of gravitational waves. They are used to build theoretical template banks for searching and analyzing the signals in the ground-based detectors LIGO and Virgo, and, further ahead, space-based LISA-like detectors. In particular, the post-Newtonian approximation describes with high accuracy the early inspiral of compact binary systems, made of black holes or neutron stars. It mainly consists of extending the Einstein quadrupole formula by a series of relativistic corrections up to high order. The compact objects are modeled by point masses with spins. The practical calculations face difficult problems of divergences, which have been solved thanks to dimensional regularization. In the last rotations before the merger, the finite size effects and the internal structure of neutron stars (notably the internal equation of state) affect the evolution of the orbit and the emission of gravitational waves. We describe these effects within a simple Newtonian model.

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Résumé

Après une brève revue des propriétés importantes des ondes gravitationnelles et de la nouvelle astronomie gravitationnelle, nous nous concentrons sur les aspects théoriques. Les méthodes d'approximation analytiques en relativité générale ont joué un rôle crucial dans les récentes détections d'ondes gravitationnelles. Elles sont utilisées pour créer des banques de modèles (patrons) théoriques qui servent à rechercher et analyser les signaux dans les détecteurs au sol LIGO et Virgo et dans les détecteurs dans l'espace de type LISA, développés plus tard. En particulier, l'approximation post-newtonienne décrit avec une grande précision le spiralement initial des systèmes binaires compacts de trous noirs ou d'étoiles à neutrons. Elle consiste principalement à étendre la formule du quadrupôle d'Einstein par une série de corrections relativistes jusqu'à un ordre élevé. Les objets compacts sont modélisés par des masses ponctuelles avec spins. Les calculs pratiques font face à des problèmes difficiles de divergences, qui ont été résolus grâce à la régularisation dimensionnelle. Dans les dernières orbites proches de la fusion, les effets de taille finie et de structure interne des étoiles à neutrons (notamment l'équation d'état interne) affectent l'évolution de l'orbite et l'émission des ondes gravitationnelles. Nous décrivons ces effets dans le cadre d'un modèle newtonien simple.

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Keywords : Gravitational waves, Compact binary systems, Post-Newtonian theory

Mots-clés : Ondes gravitationnelles, systèmes compacts binaires, théorie post-newtonienne


1  A resolution of the XXXth general assembly of the International Astronomical Union (IAU) recommended that the expansion of the Universe be referred to as the “Hubble–Lemaître law”.
2  We shall discuss an exception in Sec. 4: The internal structure and the non-gravitational equation of state of neutron stars do affect the GW signal close to and during the final merger.
3  By order n PN we refer to a small post-Newtonian term of the order of  .
4  But see the controversial debate on this point at the time of the binary pulsar [[22], [23]].
5  Because of prohibitive computing times, the NR calculations are limited to a few tens of orbits before the merger, and will likely never be competitive with the PN approximation when monitoring tens of thousands of cycles in the early inspiral.
6  See [[43]] for an history of the problems of motion and radiation, and for references to previous PN approximations.
7  Here   is the (probably irrational/transcendental) Euler's constant.
8  See Refs. [[81], [82], [83], [84], [85], [86]] for entries in the literature.


© 2019  Published by Elsevier Masson SAS de la part de Académie des sciences.
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