Luc Blanchet

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

To be observed and analyzed by the network of gravitational wave detectors on ground (LIGO, VIRGO, etc.) and by the future detectors in space (eLISA, etc.), inspiralling compact binaries — binary star systems composed of neutron stars and/or black holes in their late stage of evolution — require high-accuracy templates predicted by general relativity theory. The gravitational waves emitted by these very relativistic systems can be accurately modelled using a high-order post-Newtonian gravitational wave generation formalism. In this article, we present the current state of the art on post-Newtonian methods as applied to the dynamics and gravitational radiation of general matter sources (including the radiation reaction back onto the source) and inspiralling compact binaries. We describe the post-Newtonian equations of motion of compact binaries and the associated Lagrangian and Hamiltonian formalisms, paying attention to the self-field regularizations at work in the calculations. Several notions of innermost circular orbits are discussed. We estimate the accuracy of the post-Newtonian approximation and make a comparison with numerical computations of the gravitational self-force for compact binaries in the small mass ratio limit. The gravitational waveform and energy flux are obtained to high post-Newtonian order and the binary’s orbital phase evolution is deduced from an energy balance argument. Some landmark results are given in the case of eccentric compact binaries — moving on quasi-elliptical orbits with non-negligible eccentricity. The spins of the two black holes play an important role in the definition of the gravitational wave templates. We investigate their imprint on the equations of motion and gravitational wave phasing up to high post-Newtonian order (restricting to spin-orbit effects which are linear in spins), and analyze the post-Newtonian spin precession equations as well as the induced precession of the orbital plane.

Gravitational-Radiation Damping of Compact Binary Systems to Second Post-Newtonian order

The rate of gravitational-wave energy loss from inspiralling binary systems of compact objects of arbitrary mass is derived through second post-Newtonian (2PN) order O[(Gm/rc 2 ) 2 ] beyond the quadrupole approximation. The result has been derived by two independent calculations of the (source) multipole moments. The 2PN terms, and in particular the finite mass contribution therein (which cannot be obtained in perturbation calculations of black hole spacetimes), are shown to make a significant contribution to the accumulated phase of theoretical templates to be used in matched filtering of the data from future gravitational-wave detectors.

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.

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 (d −3) −1 ] 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�ν (x λ ). 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 3PN ambiguity parameter λ to be: λ = −1987/3080. This value is fully consistent with the recent determination of the equivalent 3PN “static ambiguity” parameter, ωs = 0, by a dimensionalregularization 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.

Higher-order spin effects in the dynamics of compact binaries. I. Equations of motion

We derive the equations of motion of spinning compact binaries including the spin-orbit (SO) coupling terms one post-Newtonian (PN) order beyond the leading-order effect. For black holes maximally spinning this corresponds to 2.5PN order. Our result for the equations of motion essentially confirms the previous result by Tagoshi, Ohashi and Owen. We also compute the spin-orbit effects up to 2.5PN order in the conserved (Noetherian) integrals of motion, namely the energy, the total angular momentum, the linear momentum and the center-of-mass integral. We obtain the spin precession equations at 1PN order beyond the leading term, as well. Those results will be used in a future paper to derive the time evolution of the binary orbital phase, providing more accurate templates for LIGO-Virgo-LISA type interferometric detectors.

Radiative gravitational fields in general relativity I. General structure of the field outside the source

We present a well-defined formal framework, together with appropriate mathematical tools, which allow us to implement in a constructive way, and to investigate in full mathematical details, the Bonnor—Thorne approach to gravitational radiation theory. We show how to construct, within this framework, the general radiative (formal) solution of the Einstein vacuum equations, in harmonic coordinates, which is both past-stationary and past-asymptotically Minkowskian. We investigate the structure of the latter general radiative metric (including all tails and nonlinear effects) both in the near zone and in the far zone. As a side result it is proven that post-Newtonian expansions must be done by using the gauge functions (lg (p,n — positive integers).

Gravitational Recoil of Inspiraling Black Hole Binaries to Second Post-Newtonian Order

The loss of linear momentum by gravitational radiation and the resulting gravitational recoil of black hole binary systems may play an important role in the growth of massive black holes in early galaxies. We calculate the gravitational recoil of nonspinning black hole binaries at the second post-Newtonian order (2 PN) beyond the dominant effect, obtaining, for the first time, the 1.5 PN correction term due to tails of waves and the next 2 PN term. We find that the maximum value of the net recoil experienced by the binary due to the inspiral phase up to the innermost stable circular orbit (ISCO) is of the order of 22 km s-1. We then estimate the kick velocity accumulated during the plunge from the ISCO up to the horizon by integrating the momentum flux using the 2 PN formula along a plunge geodesic of the Schwarzschild metric. We find that the contribution of the plunge dominates over that of the inspiral. For a mass ratio m2/m1 = , we estimate a total recoil velocity (due to both adiabatic and plunge phases) of 100 ± 20 km s-1. For a ratio of 0.38, the recoil is maximum, and we estimate it to be 250 ± 50 km s-1. In the limit of small mass ratio, we estimate V/c ≈ 0.043(±20%)(m2/m1)2. Our estimates are consistent with, but span a substantially narrower range than, those of Favata and coworkers.

General relativistic dynamics of compact binaries at the third post-Newtonian order

The general relativistic corrections in the equations of motion and associated energy of a binary system of pointlike masses are derived at the third post-Newtonian ~3PN! order. The derivation is based on a postNewtonian expansion of the metric in harmonic coordinates at the 3PN approximation. The metric is parametrized by appropriate nonlinear potentials, which are evaluated in the case of two point particles using a Lorentzian version of a Hadamard regularization which has been defined in previous works. Distributional forms and distributional derivatives constructed from this regularization are employed systematically. The equations of motion of the particles are geodesiclike with respect to the regularized metric. Crucial contributions to the acceleration are associated with the nondistributivity of the Hadamard regularization and the violation of the Leibniz rule by the distributional derivative. The final equations of motion at the 3PN order are invariant under global Lorentz transformations, and admit a conserved energy ~neglecting the radiation reaction force at the 2.5PN order!. However, they are not fully determined, as they depend on one arbitrary constant, which probably reflects a physical incompleteness of the point-mass regularization. The results of this paper should be useful when comparing theory to the observations of gravitational waves from binary systems in future detectors VIRGO and LIGO.

Quantum tests of the Einstein Equivalence Principle with the STE-QUEST space mission

We present in detail the scientific objectives in fundamental physics of the Space-Time Explorer and QUantum Equivalence Space Test (STE-QUEST) space mission. STE-QUEST was pre-selected by the European Space Agency together with four other missions for the cosmic vision M3 launch opportunity planned around 2024. It carries out tests of different aspects of the Einstein Equivalence Principle using atomic clocks, matter wave interferometry and long distance time/frequency links, providing fascinating science at the interface between quantum mechanics and gravitation that cannot be achieved, at that level of precision, in ground experiments. We especially emphasize the specific strong interest of performing equivalence principle tests in the quantum regime, i.e. using quantum atomic wave interferometry. Although STE-QUEST was finally not selected in early 2014 because of budgetary and technological reasons, its science case was very highly rated. Our aim is to expose that science to a large audience in order to allow future projects and proposals to take advantage of the STE-QUEST experience.

Relativistic theory for time and frequency transfer to order c**(-3)

This paper is motivated by the current development of several space missions (e.g. ACES on International Space Station) that will use Earth-orbit laser cooled atomic clocks, providing a time-keeping accuracy of the order of 5 10 -17 in fractional frequency. We show that to such accuracy, the theory of frequency transfer between Earth and Space must be extended from the currently known relativistic order