Corrigendum: Astrophysical and terrestrial probes to test Einstein–Cartan gravity (2001 Class. Quantum Grav. 18 3907)

As a first step in the computation of the orbital phase evolution of spinless compact binaries including tidal effects up to the next-to-next-to-leading (NNL) order, we obtain the equations of motion of those systems and the associated conserved integrals in harmonic coordinates. The internal structure and finite size effects of the compact objects are described by means of an effective Fokker-type action. Our results, complete to the NNL order, correspond to the second-post-Newtonian (2PN) approximation beyond the leading tidal effect itself, already occurring at the 5PN order. They are parametrized by three polarizability (or deformability) coefficients describing the mass quadrupolar, mass octupolar and current quadrupolar deformations of the objects through tidal interactions. Up to the next-to-leading (NL) order, we recover previous results in the literature; up to the NNL order for quasi-circular orbits, we confirm the known tidal effects in the (PN re-expansion of the) effective-one-body (EOB) Hamiltonian. In a future work, we shall derive the tidal contributions to the gravitational-wave flux up to the NNL order, which is the second step required to find the orbital phase evolution. * quentin.henry@iap.fr †

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“…We obtain G i = G i pp + G i tidal , where the point-particle piece is given by Eq. (4.4) in [43], i.e. at the 1PN order by…”

Section: Tidal Effects In the Equations Of Motion To Nnl Ordermentioning

confidence: 97%

Tidal effects in the equations of motion of compact binary systems to next-to-next-to-leading post-Newtonian order

2020

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“…We have also obtained the conserved quantities by an alternative Lagrangian method, as described in [21], and we have checked that the two methods give the same results. Using the center-of-mass coordinates (3.7)-(3.9) derived in the previous section, we can write these quantities in the CM frame.…”

Section: A Local Partmentioning

confidence: 99%

Dynamics of compact binary systems in scalar-tensor theories. II. Center-of-mass and conserved quantities to 3PN order

Bernard

2019

Phys. Rev. D

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The equations of motion of nonspinning compact binary systems at the third post-Newtonian (PN) order in massless scalar-tensor theories have recently been obtained. In the present paper, we complete this work by computing at 3PN order the ten integrals of motion together with the equations of motion in the center-of-mass frame. We then perform the reduction of the center-of-mass equations to quasi-circular orbits and determine the conserved energy and angular momentum for circular orbits. I. INTRODUCTIONThe detections of gravitational waves emitted by inspiralling compact binaries is a first step towards a better comprehension of gravitational physics [1]. In the future, the next generation of high precision experiments will allow a better understanding of these systems, by constraining their abundance, origin and parameters. It will also provide information about the strong-field and highly-dynamical regime of gravitational physics, by challenging the theory of general relativity (GR) in this regime.The detection and parameter estimation of gravitational wave events require a bank of highly accurate templates for the gravitational waveforms, to be match-filtered against the data. Current templates are constructed by matching the waveform at different stages of the coalescence, that are obtained using different approaches: post-Newtonian formalism for the inspiral [2] and numerical relativity for the merger and ringdown [3]. There are currently two main series of template waveforms to be used by the LIGO-Virgo collaboration, based either on a direct matching (IMR models) [4,5] or on some resummation techniques (EOB waveforms) [6,7].In order to perform tests of general relativity, one also has to construct such templates for the many alternative theories of gravity. There exist two different and complementary approaches to this problem: either theoryindependent [8] or theory-dependent [9]. Although fundamentally different, these two approaches are complementary as one needs to be able to map the constraints coming from the agnostic approach to specific theories. Here, we will focus on a specific model, namely massless scalar-tensor theory [10,11], one of the oldest, most popular and well-studied theory of gravity [12]. It consists in adding a single massless scalar field, coupled in a minimal way to gravity. One of the motivations for studying this theory, which usually arises as a low-energy limit of some string theory, relies on the fact that it may explain the accelerated expansion of the universe [13].The present work is part of a series of articles whose attempt is to construct the full gravitational and scalar waveforms in scalar-tensor theories up to 2PN order 1 [14-17]. In the companion paper [17], that will be referred to as Paper I in the following, we computed the harmonic coordinate equations of motion in scalar-tensor theories at 3PN order. In the present paper, we complete this work by determining the center-of-mass and conserved quantities to the same 3PN order in the center-of-mass frame. As the le...

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“…We are, therefore, confident that the power of the proposed test is not diminished by this assumption. The conserved energy (per unit mass) up to 3PN order is given by [66,[78][79][80][81][82][83]…”

Section: B Conservative Dynamics Of the Binarymentioning

confidence: 99%

Testing the multipole structure of compact binaries using gravitational wave observations

et al. 2018

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We propose a novel method to test the consistency of the multipole moments of compact binary systems with the predictions of general relativity (GR). The multipole moments of a compact binary system, known in terms of symmetric and trace-free tensors, are used to calculate the gravitational waveforms from compact binaries within the post-Newtonian (PN) formalism. For nonspinning compact binaries, we derive the gravitational wave phasing formula, in the frequency domain, parametrizing each PN order term in terms of the multipole moments which contribute to that order. Using GW observations, this parametrized multipolar phasing would allow us to derive the bounds on possible departures from the multipole structure of GR and hence constrain the parameter space of alternative theories of gravity. We compute the projected accuracies with which the second-generation ground-based detectors, such as the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO), the third-generation detectors such as the Einstein Telescope and Cosmic Explorer, as well as the space-based detector Laser Interferometer Space Antenna (LISA) will be able to measure these multipole parameters. We find that while Advanced LIGO can measure the first two or three multipole coefficients with good accuracy, Cosmic Explorer and the Einstein Telescope may be able to measure the first four multipole coefficients which enter the phasing formula. Intermediate-mass-ratio inspirals, with mass ratios of several tens, in the frequency band of the planned space-based LISA mission should be able to measure all seven multipole coefficients which appear in the 3.5PN phasing formula. Our finding highlights the importance of this class of sources for probing the strong-field gravity regime. The proposed test will facilitate the first probe of the multipolar structure of Einstein's general relativity. * shilpakastha@imsc.res.in † axg645@psu.edu ‡ kgarun@cmi.ac.in § bss25@psu.edu ¶ vdbroeck@nikhef.nl arXiv:1809.10465v2 [gr-qc]

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Corrigendum: Astrophysical and terrestrial probes to test Einstein–Cartan gravity (2001 Class. Quantum Grav. 18 3907)

Cited by 18 publications

References 7 publications

Tidal effects in the equations of motion of compact binary systems to next-to-next-to-leading post-Newtonian order

Tidal effects in the equations of motion of compact binary systems to next-to-next-to-leading post-Newtonian order

Dynamics of compact binary systems in scalar-tensor theories. II. Center-of-mass and conserved quantities to 3PN order

Testing the multipole structure of compact binaries using gravitational wave observations

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