arXiv subjects

Luc Blanchet

Publications and source records attributed to Luc Blanchet.

At least 127 records · Page 7Linked to original sources

arXiv2005

Gravitational-wave tails of tails

The tails of gravitational waves are caused by scattering of linear waves onto the space-time curvature generated by the total mass-energy of the source. Quite naturally, the tails of tails are caused by curvature scattering of the tails of waves themselves. The tails of tails are associated with the cubic non-linear interaction between two mass monopole moments and, dominantly, the mass quadrupole of the source. In this paper we determine the radiation field at large distances from the source for this particular monopole-monopole-quadrupole interaction. We find that the tails of tails appear at the third post-Newtonian (3PN) order beyond the usual quadrupole radiation. Motivated by the need of accurate templates to be used in the data analysis of future detectors of gravitational waves, we compute the contribution of tails, and of tails of tails, up to the 3.5PN order in the energy flux generated by inspiraling compact binaries.

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arXiv2005

The 2.5PN gravitational wave polarisations from inspiralling compact binaries in circular orbits

Using the multipolar post-Minkowskian and matching formalism we compute the gravitational waveform of inspiralling compact binaries moving in quasi-circular orbits at the second and a half post-Newtonian (2.5PN) approximation to general relativity. The inputs we use include notably the mass-type quadrupole at the 2.5PN order, the mass octupole and current quadrupole at the 2PN order, the mass $2^5$-pole and current $2^4$-pole at 1PN. The non-linear hereditary terms come from the monopole-quadrupole multipole interactions or tails, present at the 1.5PN, 2PN and 2.5PN orders, and the quadrupole-quadrupole interaction arising at the 2.5PN level. In particular, the specific effect of non-linear memory is computed using a simplified model of binary evolution in the past. The ``plus'' and ``cross'' wave polarisations at the 2.5PN order are obtained in ready-to-use form, extending the 2PN results calculated earlier by Blanchet, Iyer, Will and Wiseman.

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arXiv2005

Energy losses by gravitational radiation in inspiralling compact binaries to five halves post-Newtonian order

This paper derives the total power or energy loss rate generated in the form of gravitational waves by an inspiralling compact binary system to the five halves post-Newtonian (2.5PN) approximation of general relativity. Extending a recently developed gravitational-wave generation formalism valid for arbitrary (slowly-moving) systems, we compute the mass multipole moments of the system and the relevant tails present in the wave zone to 2.5PN order. In the case of two point-masses moving on a quasi-circular orbit, we find that the 2.5PN contribution in the energy loss rate is entirely due to tails. Relying on an energy balance argument we derive the laws of variation of the instantaneous frequency and phase of the binary. The 2.5PN order in the accumulated phase is significantly large, being grossly of the same order of magnitude as the previous 2PN order, but opposite in sign. However finite mass effects at 2.5PN order are small. The results of this paper should be useful when analyzing the data from inspiralling compact binaries in future gravitational-wave detectors like VIRGO and LIGO.

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arXiv2005

Gravitational-Wave Inspiral of Compact Binary Systems to 7/2 Post-Newtonian Order

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 energy and emitted gravitational flux. The analysis consistently includes the relativistic effects in the binary's equations of motion and multipole moments, as well as the contributions of tails, and tails of tails, in the wave zone. However the result is not fully determined because of some physical incompleteness, present at the 3PN order, of the model of point-particle and the associated Hadamard-type self-field regularization. The orbital phase, whose prior knowledge is crucial for searching and analyzing the inspiral signal, is computed from the standard energy balance argument.

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arXiv2005

Gravitational waves from inspiralling compact binaries: Energy flux to third post-Newtonian order

The multipolar-post-Minkowskian approach to gravitational radiation is applied to the problem of the generation of waves by the compact binary inspiral. We investigate specifically the third post-Newtonian (3PN) approximation in the total energy flux. The new results are the computation of the mass quadrupole moment of the binary to the 3PN order, and the current quadrupole and mass octupole to the 2PN order. Wave tails and tails of tails in the far zone are included up to the 3.5PN order. The recently derived 3PN equations of binary motion are used to compute the time-derivatives of the moments. We find perfect agreement to the 3.5PN order with perturbation calculations of black holes in the test-mass limit for one body. Technical inputs in our computation include a model of point particles for describing the compact objects, and the Hadamard self-field regularization. Because of a physical incompleteness of the Hadamard regularization at the 3PN order, the energy flux depends on one unknown physical parameter, which is a combination of a parameter λin the equations of motion, and a new parameter θcoming from the quadrupole moment.

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arXiv2005

Dimensional regularization of the third post-Newtonian gravitational wave generation from two point masses

Dimensional regularization is applied to the computation of the gravitational wave field generated by compact binaries at the third post-Newtonian (3PN) approximation. We generalize the wave generation formalism from isolated post-Newtonian matter systems to d spatial dimensions, and apply it to point masses (without spins), modelled by delta-function singularities. We find that the quadrupole moment of point-particle binaries in harmonic coordinates contains a pole when epsilon = d-3 -> 0 at the 3PN order. It is proved that the pole can be renormalized away by means of the same shifts of the particle world-lines as in our recent derivation of the 3PN equations of motion. The resulting renormalized (finite when epsilon -> 0) quadrupole moment leads to unique values for the ambiguity parameters xi, kappa and zeta, which were introduced in previous computations using Hadamard's regularization. Several checks of these values are presented. These results complete the derivation of the gravitational waves emitted by inspiralling compact binaries up to the 3.5PN level of accuracy which is needed for detection and analysis of the signals in the gravitational-wave antennas LIGO/VIRGO and LISA.

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arXiv2005

Gravitational radiation reaction in the equations of motion of compact binaries to 3.5 post-Newtonian order

We compute the radiation reaction force on the orbital motion of compact binaries to the 3.5 post-Newtonian (3.5PN) approximation, i.e. one PN order beyond the dominant effect. The method is based on a direct PN iteration of the near-zone metric and equations of motion of an extended isolated system, using appropriate ``asymptotically matched'' flat-space-time retarded potentials. The formalism is subsequently applied to binary systems of point particles, with the help of the Hadamard self-field regularisation. Our result is the 3.5PN acceleration term in a general harmonic coordinate frame. Restricting the expression to the centre-of-mass frame, we find perfect agreement with the result derived in a class of coordinate systems by Iyer and Will using the energy and angular momentum balance equations.

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arXiv2004

Hadamard regularization of the third post-Newtonian gravitational wave generation of two point masses

Continuing previous work on the 3PN-accurate gravitational wave generation from point particle binaries, we obtain the binary's 3PN mass-type quadrupole and dipole moments for general (not necessarily circular) orbits in harmonic coordinates. The final expressions are given in terms of their ``core'' parts, resulting from the application of the pure Hadamard-Schwartz (pHS) self-field regularization scheme, and augmented by an ``ambiguous'' part. In the case of the 3PN quadrupole we find three ambiguity parameters, xi, kappa and zeta, but only one for the 3PN dipole, in the form of the particular combination xi+kappa. Requiring that the dipole moment agree with the center-of-mass position deduced from the 3PN equations of motion in harmonic coordinates yields the relation xi+kappa=-9871/9240. Our results will form the basis of the complete calculation of the 3PN radiation field of compact binaries by means of dimensional regularization.

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arXiv2004

Surface-integral expressions for the multipole moments of post-Newtonian sources and the boosted Schwarzschild solution

New expressions for the multipole moments of an isolated post-Newtonian source, in the form of surface integrals in the outer near-zone, are derived. As an application we compute the ``source'' quadrupole moment of a Schwarzschild solution boosted to uniform velocity, at the third post-Newtonian (3PN) order. We show that the consideration of this boosted Schwarzschild solution (BSS) is enough to uniquely determine one of the ambiguity parameters in the recent computation of the gravitational wave generation by compact binaries at 3PN order: zeta=-7/33. We argue that this value is the only one for which the Poincaré invariance of the 3PN wave generation formalism is realized. As a check, we confirm the value of zeta by a different method, based on the far-zone expansion of the BSS at fixed retarded time, and a calculation of the relevant non-linear multipole interactions in the external metric at the 3PN order.

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arXiv2004

Gravitational radiation from inspiralling compact binaries completed at the third post-Newtonian order

The gravitational radiation from point particle binaries is computed at the third post-Newtonian (3PN) approximation of general relativity. Three previously introduced ambiguity parameters, coming from the Hadamard self-field regularization of the 3PN source-type mass quadrupole moment, are consistently determined by means of dimensional regularization, and proved to have the values xi = -9871/9240, kappa = 0 and zeta = -7/33. These results complete the derivation of the general relativistic prediction for compact binary inspiral up to 3.5PN order, and should be of use for searching and deciphering the signals in the current network of gravitational wave detectors.

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arXiv2004

Dimensional regularization of the third post-Newtonian dynamics of point particles in harmonic coordinates

Dimensional regularization is used to derive the equations of motion of two point masses in harmonic coordinates. At the third post-Newtonian (3PN) approximation, it is found that the dimensionally regularized equations of motion contain a pole part [proportional to 1/(d-3)] which diverges as the space dimension d tends to 3. It is proven that the pole part can be renormalized away by introducing suitable shifts of the two world-lines representing the point masses, and that the same shifts renormalize away the pole part of the "bulk" metric tensor g_munu(x). The ensuing, finite renormalized equations of motion are then found to belong to the general parametric equations of motion derived by an extended Hadamard regularization method, and to uniquely determine the heretofore unknown 3PN parameter lambda to be: lambda = - 1987/3080. This value is fully consistent with the recent determination of the equivalent 3PN static ambiguity parameter, omega_s = 0, by a dimensional-regularization derivation of the Hamiltonian in Arnowitt-Deser-Misner coordinates. Our work provides a new, powerful check of the consistency of the dimensional regularization method within the context of the classical gravitational interaction of point particles.

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arXiv2004

Equations of motion of compact binaries at the third post-Newtonian order

The equations of motion of two point masses in harmonic coordinates are derived through the third post-Newtonian (3PN) approximation. The problem of self-field regularization (necessary for removing the divergent self-field of point particles) is dealt with in two separate steps. In a first step the extended Hadamard regularization is applied, resulting in equations of motion which are complete at the 3PN order, except for the occurence of one and only one unknown parameter. In a second step the dimensional regularization (in d dimensions) is used as a powerful argument for fixing the value of this parameter, thereby completing the 3-dimensional Hadamard-regularization result. The complete equations of motion and associated energy at the 3PN order are given in the case of circular orbits.

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arXiv2003

Time-symmetric initial data for binary black holes in numerical relativity

We look for physically realistic initial data in numerical relativity which are in agreement with post-Newtonian approximations. We propose a particular solution of the time-symmetric constraint equation, appropriate to two momentarily static black holes, in the form of a conformal decomposition of the spatial metric. This solution is isometric to the post-Newtonian metric up to the 2PN order. It represents a non-linear deformation of the solution of Brill and Lindquist, i.e. an asymptotically flat region is connected to two asymptotically flat (in a certain weak sense) sheets, that are the images of the two singularities through appropriate inversion transformations. The total ADM mass M as well as the individual masses m_1 and m_2 (when they exist) are computed by surface integrals performed at infinity. Using second order perturbation theory on the Brill-Lindquist background, we prove that the binary's interacting mass-energy M-m_1-m_2 is well-defined at the 2PN order and in agreement with the known post-Newtonian result.

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arXiv2003

On the accuracy of the post-Newtonian approximation

We apply standard post-Newtonian methods in general relativity to locate the innermost circular orbit (ICO) of irrotational and corotational binary black-hole systems. We find that the post-Newtonian series converges well when the two masses are comparable. We argue that the result for the ICO which is predicted by the third post-Newtonian (3PN) approximation is likely to be very close to the ``exact'' solution, within 1% of fractional accuracy or better. The 3PN result is also in remarkable agreement with a numerical calculation of the ICO in the case of two corotating black holes moving on exactly circular orbits. The behaviour of the post-Newtonian series suggests that the gravitational dynamics of two bodies of comparable masses does not resemble that of a test particle on a Schwarzschild background. This leads us to question the validity of some post-Newtonian resummation techniques that are based on the idea that the field generated by two black holes is a deformation of the Schwarzschild space-time.

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arXiv2003

Post-Newtonian Theory and its Application

We review some recent works on the post-Newtonian theory of slowly-moving (post-Newtonian) sources, and its application to the problems of dynamics and gravitational radiation from compact binary systems. Our current knowledge is 3PN on the center-of-mass energy and 3.5PN on the gravitational-wave flux of inspiralling compact binaries. We compute the innermost circular orbit (ICO) of binary black-hole systems and find a very good agreement with the result of numerical relativity. We argue that the gravitational dynamics of two bodies of comparable masses in general relativity does not resemble that of a test particle on a Schwarzschild background. This leads us to question the validity of some ``Schwarzschild-like'' templates for binary inspiral which are constructed from post-Newtonian resummation techniques.

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arXiv2003

Third post-Newtonian dynamics of compact binaries: Equations of motion in the center-of-mass frame

The equations of motion of compact binary systems and their associated Lagrangian formulation have been derived in previous works at the third post-Newtonian (3PN) approximation of general relativity in harmonic coordinates. In the present work we investigate the binary's relative dynamics in the center-of-mass frame (center of mass located at the origin of the coordinates). We obtain the 3PN-accurate expressions of the center-of-mass positions and equations of the relative binary motion. We show that the equations derive from a Lagrangian (neglecting the radiation reaction), from which we deduce the conserved center-of-mass energy and angular momentum at the 3PN order. The harmonic-coordinates center-of-mass Lagrangian is equivalent, {\it via} a contact transformation of the particles' variables, to the center-of-mass Hamiltonian in ADM coordinates that is known from the post-Newtonian ADM-Hamiltonian formalism. As an application we investigate the dynamical stability of circular binary orbits at the 3PN order.

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arXiv2002

Innermost circular orbit of binary black holes at the third post-Newtonian approximation

The equations of motion of two point masses have recently been derived at the 3PN approximation of general relativity. From that work we determine the location of the innermost circular orbit or ICO, defined by the minimum of the binary's 3PN energy as a function of the orbital frequency for circular orbits. We find that the post-Newtonian series converges well for equal masses. Spin effects appropriate to corotational black-hole binaries are included. We compare the result with a recent numerical calculation of the ICO in the case of two black holes moving on exactly circular orbits (helical symmetry). The agreement is remarkably good, indicating that the 3PN approximation is adequate to locate the ICO of two black holes with comparable masses. This conclusion is reached with the post-Newtonian expansion expressed in the standard Taylor form, without using resummation techniques such as Padé approximants and/or effective-one-body methods.

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arXiv2002

Post-Newtonian approximation for isolated systems calculated by matched asymptotic expansions

Two long-standing problems with the post-Newtonian approximation for isolated slowly-moving systems in general relativity are: (i) the appearance at high post-Newtonian orders of divergent Poisson integrals, casting a doubt on the soundness of the post-Newtonian series; (ii) the domain of validity of the approximation which is limited to the near-zone of the source, and prevents one, a priori, from incorporating the condition of no-incoming radiation, to be imposed at past null infinity. In this article, we resolve the problem (i) by iterating the post-Newtonian hierarchy of equations by means of a new (Poisson-type) integral operator that is free of divergencies, and the problem (ii) by matching the post-Newtonian near-zone field to the exterior field of the source, known from previous work as a multipolar-post-Minkowskian expansion satisfying the relevant boundary conditions at infinity. As a result, we obtain an algorithm for iterating the post-Newtonian series up to any order, and we determine the terms, present in the post-Newtonian field, that are associated with the gravitational-radiation reaction onto an isolated slowly-moving matter system.

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