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In this manuscript we review the theoretical foundations of gravitational waves in the framework of Albert Einstein's theory of general relativity. Following Einstein's early efforts we first derive the linearised Einstein field equations…

General Relativity and Quantum Cosmology · Physics 2018-05-22 Alain Dirkes

The paper generalizes the structure of gravitational waves from orbiting spinning binaries under leading order spin-orbit coupling, as given in the work by K\"onigsd\"orffer and Gopakumar [PRD 71, 024039 (2005)] for single-spin and…

General Relativity and Quantum Cosmology · Physics 2015-05-14 Manuel Tessmer

The emission of gravitational waves from a system of massive objects interacting on elliptical, hyperbolic and parabolic orbits is studied in the quadrupole approximation. Analytical expressions are then derived for the gravitational wave…

General Relativity and Quantum Cosmology · Physics 2009-06-29 M. De Laurentis , S. Capozziello

The emission of gravitational waves from a system of massive objects interacting on elliptical, hyperbolic and parabolic orbits is studied in the quadrupole approximation. Analytical expressions are then derived for the gravitational wave…

Astrophysics · Physics 2010-04-21 Salvatore Capozziello , Mariafelicia De Laurentis

We study gravitational waves emitted by a binary system of non-spinning bodies in a quasi-circular inspiral within the framework of Einstein-aether theory. In particular, we compute explicitly and analytically the expressions for the…

General Relativity and Quantum Cosmology · Physics 2021-10-22 Chao Zhang , Xiang Zhao , Anzhong Wang , Bin Wang , Kent Yagi , Nicolas Yunes , Wen Zhao , Tao Zhu

A binary system, composed of a compact object orbiting around a massive central body, will emit gravitational waves which will depend on the central body's spacetime geometry. We expect that the gravitational wave observables will somehow…

General Relativity and Quantum Cosmology · Physics 2009-11-11 Thomas P. Sotiriou , Theocharis A. Apostolatos

This paper is motivated by the need to improve the post-Newtonian (PN) amplitude accuracy of waveforms for gravitational waves generated by inspiralling compact binaries, both for use in data analysis and in the comparison between…

General Relativity and Quantum Cosmology · Physics 2015-06-22 Guillaume Faye , Luc Blanchet , Bala R. Iyer

After a short review of prominent properties of gravitational waves and the newly born gravitational astronomy, we focus on theoretical aspects. Analytic approximation methods in general relativity have played a crucial role in the recent…

General Relativity and Quantum Cosmology · Physics 2020-01-08 Luc Blanchet

We report application of a method for extracting gravitational waves to three-dimensional numerical simulation on coalescing binary neutron stars. We found the extracted wave form includes the componets corresponding to the quadrupole part…

Astrophysics · Physics 2009-11-10 Mari Kawamura , Ken-ichi Oohara

In this work we analyze the emission of gravitational waves from a gravitational system described by a Newtonian term plus a H\'enon-Heiles term. The main concern is to analyze how the inclusion of the Newtonian term changes the emission of…

General Relativity and Quantum Cosmology · Physics 2009-10-31 F. Kokubun

We have introduced a new method for computing gravitational-wave emission from nonspinning binaries which systematically unifies the various integrals arising in the Fourier expansions of post-Newtonian dynamics, providing a simple,…

General Relativity and Quantum Cosmology · Physics 2025-12-16 Xiaolin Liu , Zhoujian Cao

In this paper we consider the Extra-solar Planetary Systems recently discovered in our Galaxy as potential sources of gravitational waves. We estimate the frequency and characteristic amplitude of the radiation they emit due to the orbital…

Astrophysics · Physics 2009-10-31 Valeria Ferrari , Marco D'Andrea , Emanuele Berti

The inspiral of compact binaries, driven by gravitational-radiation reaction, is investigated through 7/2 post-Newtonian (3.5PN) order beyond the quadrupole radiation. We outline the derivation of the 3.5PN-accurate binary's center-of-mass…

General Relativity and Quantum Cosmology · Physics 2014-11-17 Luc Blanchet , Guillaume Faye , Bala R. Iyer , Benoit Joguet

Gravitational waves contain tail effects that are due to the backscattering of linear waves in the curved space-time geometry around the source. The knowledge as well as the accuracy of the two-body inspiraling post-Newtonian (PN) dynamics…

General Relativity and Quantum Cosmology · Physics 2012-10-03 Luc Blanchet , Alessandra Buonanno , Guillaume Faye

We present a systematic and robust approach to nonlinear gravitational perturbations of vacuum spacetimes. This approach provides a basis for a theory of nonlinear gravitational waves. In particular, we show that the system of perturbative…

General Relativity and Quantum Cosmology · Physics 2017-12-27 Andrzej Rostworowski

We compute the third post-Newtonian (3PN) accurate instantaneous contributions to the radiated gravitational wave (GW) energy and angular momentum arising from the hyperbolic passages of non-spinning compact objects. The present…

General Relativity and Quantum Cosmology · Physics 2022-04-21 Gihyuk Cho , Subhajit Dandapat , Achamveedu Gopakumar

The inspiral phase of gravitational waves emitted by spinless compact binary systems is derived through the fourth-and-a-half post-Newtonian (4.5PN) order beyond quadrupole radiation, and the leading amplitude mode ($\ell$, m) = (2, 2) is…

General Relativity and Quantum Cosmology · Physics 2023-10-03 Luc Blanchet , Guillaume Faye , Quentin Henry , François Larrouturou , David Trestini

We study gravitational waves from a hierarchical three-body system up to first-order postNewtonian approximation. Under certain conditions, the existence of a nearby third body can cause periodic exchange between eccentricity of an inner…

General Relativity and Quantum Cosmology · Physics 2020-05-27 Priti Gupta , Haruka Suzuki , Hirotada Okawa , Kei-ichi Maeda

Gravitational waveforms and production could be considerably affected by gravitomagnetic corrections considered in relativistic theory of orbits. Beside the standard periastron effect of General Relativity, new nutation effects come out…

General Relativity and Quantum Cosmology · Physics 2015-05-14 S. Capozziello , M. De Laurentis , L. Forte , F. Garufi , L. Milano

Accurate parameter estimation of gravitational waves from coalescing compact binary sources is a key requirement for gravitational-wave astronomy. Evaluating the posterior probability density function of the binary's parameters (component…

High Energy Astrophysical Phenomena · Physics 2015-06-12 R. J. E. Smith , K. Cannon , C. Hanna , D. Keppel , I. Mandel