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García, Alfredo Martín

doi:10.3989/revindias.2002.i225.479

Cited by 4 publications

(6 citation statements)

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“…Throughout this paper, we have used xTensor, xCoba and TexAct, all parts of the Mathematica package xAct available in Ref. [28]. We wish to thank L. Bernard, C. Deffayet, G. Esposito-Farèse, L. Heisenberg and G. Faye for illuminating discussions.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Generalized Proca action for an Abelian vector field

Allys

Peter

Rodríguez

2016

J. Cosmol. Astropart. Phys.

178

187

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We revisit the most general theory for a massive vector field with derivative self-interactions, extending previous works on the subject to account for terms having trivial total derivative interactions for the longitudinal mode. In the flat spacetime (Minkowski) case, we obtain all the possible terms containing products of up to five first-order derivatives of the vector field, and provide a conjecture about higher-order terms. Rendering the metric dynamical, we covariantize the results and add all possible terms implying curvature. * Electronic address: allys@iap.fr † Electronic address: peter@iap.fr ‡ Electronic address: yeinzon.rodriguez@uan.edu.co 1 It is a subset in the multi-field case. 2 Some general works on general ghost-free Lagrangians published recently, see Refs. [16,17], can also be applied to the generalization of the Proca theory. 4 Here and in what follows, we denote by ǫ σ 1 σ 2 ...σ D the totally antisymmetric Levi-Civita tensor in D dimensions (in the case D = 4 we are concerned with in the rest of this paper, we write ǫ µναβ ).

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Section: Acknowledgmentsmentioning

confidence: 99%

Generalized Proca action for an Abelian vector field

Allys

Peter

Rodríguez

2016

J. Cosmol. Astropart. Phys.

178

187

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“…This work was supported by the NASA grant 11-ATP-046, as well as the NASA grant NNX12AN10G at the University of Maryland College Park. Some of our computations were done using Mathematica® and the symbolic tensor calculus package xAct [103].…”

Section: Acknowledgmentsmentioning

confidence: 99%

Cubic-order spin effects in the dynamics and gravitational wave energy flux of compact object binaries

Marsat

2015

Class. Quantum Grav.

101

157

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We investigate cubic-in-spin effects for inspiralling compact objects binaries, both in the dynamics and the energy flux emitted in gravitational waves, at the leading post-Newtonian order. We use a Lagrangian formalism to implement finite-size effects, and extend it at cubic order in the spins, which corresponds to the octupolar order in a multipolar decomposition. This formalism allows us to derive the equation of motion, equations of precession for the spin, and stress-energy tensor of each body in covariant form, and admits a formal generalization to any multipolar order. For spin-induced multipoles, i.e. in the case where the rotation of the compact object is sole responsible for the additional multipole moments, we find a unique structure for the octupolar moment representing cubic-in-spin effects. We apply these results to compute the associated effects in the dynamics of compact binary systems, and deduce the corresponding terms in the energy loss rate due to gravitational waves. These effects enter at the third-and-a-half post-Newtonian order, and can be important for binaries involving rapidly spinning black holes. We provide simplified results for spin-aligned, circular orbits, and discuss the quantitative importance of the new contributions.

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“…(5.1) 17 We have implemented the MPM algorithm on the algebraic computing software Mathematica using the powerful tensor package xTensor [55].…”

Section: The Radiative Moments For 3pn Polarizationsmentioning

confidence: 99%

“…A part of the results of this paper was obtained by means of the tensor package xTensor developed for Mathematica by J Martín-García [55]. We thank him for the technical support he provided as we were elaborating the code.…”

Section: Acknowledgmentsmentioning

confidence: 99%

The third post-Newtonian gravitational wave polarizations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits

Blanchet

Faye

Iyer

et al. 2008

Class. Quantum Grav.

237

401

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The gravitational waveform (GWF) generated by inspiralling compact binaries moving in quasicircular orbits is computed at the third post-Newtonian (3PN) approximation to general relativity. Our motivation is two-fold: (i) To provide accurate templates for the data analysis of gravitational wave inspiral signals in laser interferometric detectors; (ii) To provide the associated spin-weighted spherical harmonic decomposition to facilitate comparison and match of the high post-Newtonian prediction for the inspiral waveform to the numerically-generated waveforms for the merger and ringdown. This extension of the GWF by half a PN order (with respect to previous work at 2.5PN order) is based on the algorithm of the multipolar post-Minkowskian formalism, and mandates the computation of the relations between the radiative, canonical and source multipole moments for general sources at 3PN order. We also obtain the 3PN extension of the source multipole moments in the case of compact binaries, and compute the contributions of hereditary terms (tails, tails-oftails and memory integrals) up to 3PN order. The end results are given for both the complete plus and cross polarizations and the separate spin-weighted spherical harmonic modes.

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Cited by 4 publications

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Generalized Proca action for an Abelian vector field

Generalized Proca action for an Abelian vector field

Cubic-order spin effects in the dynamics and gravitational wave energy flux of compact object binaries

The third post-Newtonian gravitational wave polarizations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits

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