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Thibault Damour

Publications and source records attributed to Thibault Damour.

At least 91 records · Page 5Linked to original sources
arXiv2015

1974: the discovery of the first binary pulsar

The 1974 discovery, by Russell A. Hulse and Joseph H. Taylor, of the first binary pulsar PSR B1913+16, opened up new possibilities for the study of relativistic gravity. PSR B1913+16, as well as several other binary pulsars, provided {\it direct} observational proofs that gravity propagates at the velocity of light and has a quadrupolar structure. Binary pulsars also provided accurate tests of the strong-field regime of relativistic gravity. General Relativity has passed all the binary pulsar tests with flying colors. The discovery of binary pulsars had also very important consequences for astrophysics: accurate measurement of neutron star masses, improved understanding of the possible evolution scenarios for the co-evolution of binary stars, proof of the existence of binary neutron stars emitting gravitational waves for hundreds of millions of years, before coalescing in catastrophic events radiating intense gravitational-wave signals, and probably leading also to important emissions of electromagnetic radiation and neutrinos. This article reviews the history of the discovery of the first binary pulsar, and describes both its immediate impact, and its longer-term effect on theoretical and experimental studies of relativistic gravity.

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arXiv2014

Gravitational self-force corrections to two-body tidal interactions and the effective one-body formalism

Tidal interactions have a significant influence on the late dynamics of compact binary systems, which constitute the prime targets of the upcoming network of gravitational-wave detectors. We refine the theoretical description of tidal interactions (hitherto known only to the second post-Newtonian level) by extending our recently developed analytic self-force formalism, for extreme mass-ratio binary systems, to the computation of several tidal invariants. Specifically, we compute, to linear order in the mass ratio and to the 7.5$^{\rm th}$ post-Newtonian order, the following tidal invariants: the square and the cube of the gravitoelectric quadrupolar tidal tensor, the square of the gravitomagnetic quadrupolar tidal tensor, and the square of the gravitoelectric octupolar tidal tensor. Our high-accuracy analytic results are compared to recent numerical self-force tidal data by Dolan et al. \cite{Dolan:2014pja}, and, notably, provide an analytic understanding of the light ring asymptotic behavior found by them. We transcribe our kinematical tidal-invariant results in the more dynamically significant effective one-body description of the tidal interaction energy. By combining, in a synergetic manner, analytical and numerical results, we provide simple, accurate analytic representations of the global, strong-field behavior of the gravitoelectric quadrupolar tidal factor. A striking finding is that the linear-in-mass-ratio piece in the latter tidal factor changes sign in the strong-field domain, to become negative (while its previously known second post-Newtonian approximant was always positive). We, however, argue that this will be more than compensated by a probable fast growth, in the strong-field domain, of the nonlinear-in-mass-ratio contributions in the tidal factor.

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arXiv2014

A new analytic representation of the ringdown waveform of coalescing spinning black hole binaries

We propose a new way of analyzing, and analytically representing, the ringdown part of the gravitational wave signal emitted by coalescing black hole binaries.By contrast with the usual {\it linear} decomposition of the multipolar complex waveform $h(t)$ in a sum of quasi-normal modes, our procedure relies on a {\it multiplicative} decomposition of $h(t)$ as the product of the fundamental quasi-normal mode with a remaining time-dependent complex factor whose amplitude and phase are separately fitted. As an illustrative example, we apply our analysis and fitting procedure to the ringdown part of a sample of sixteen $\ell=m=2$ equal-mass, spinning, nonprecessing, numerical waveforms computed with the SP$_{\rm E}$C code,now publicly available in the SXS catalogue. Our approach yields an efficient and accurate way to represent the ringdown waveform, thereby offering a new way to complete the analytical effective-one-body inspiral-plus-plunge waveform.

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arXiv2014

A new effective-one-body description of coalescing nonprecessing spinning black-hole binaries

We present a new, tunable effective-one-body (EOB) model of the motion and radiation of coalescing black hole binaries with arbitrary mass ratio and aligned spins. The most novel feature of our formalism is the introduction, and systematic use, of the (gauge-invariant) concept of {\it centrifugal radius} $r_{c}$. In the spinning small mass-ratio limit, the main radial potential expressed in terms of $r_{c}$ differs very little (and only multiplicatively so) from the usual Schwarzschild potential $1-2M/r_{c}$. This motivates a new, multiplicative way of blending finite-mass-ratio deformations with spin-deformations. In the present exploratory work we consider a minimal version of our spinning EOB model (containing essentially only two adjustable parameters: one in the Hamiltonian and one in the waveform) and calibrate its (dominant mode) waveform against a sample of fifteen equal-mass, equal-spin waveforms produced by the SXS collaboration, and covering the dimensionless spin range $-0.95\leq χ\leq +0.98$. The numerical relativity / EOB phasing disagreement remains remarkably small ($\lesssim \pm 0.15$ rad) over the entire spin range.

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arXiv2014

Quantum Supersymmetric Bianchi IX Cosmology

We study the quantum dynamics of a supersymmetric squashed three-sphere by dimensionally reducing to one timelike dimension the action of D=4 simple supergravity for a Bianchi IX cosmological model. After imposition of the diffeomorphism constraints, the wave function of the Universe becomes a spinor of Spin(8,4) depending on the three squashing parameters, which satisfies Dirac, and Klein-Gordon-like, wave equations describing the propagation of a quantum spinning particle reflecting off spin-dependent potential walls. The algebra of the susy constraints and of the Hamiltonian one is found to close. One finds that the quantum Hamiltonian is built from operators that generate a 64-dimensional representation of the maximally compact sub-algebra of the rank-3 hyperbolic Kac-Moody algebra AE3. The (quartic-in-fermions) squared-mass term entering the Klein-Gordon-like equation has several remarkable properties: 1)it commutes with all the other (Kac-Moody-related) building blocks of the Hamiltonian; 2)it is a quadratic function of the fermion number NF; 3)it is negative in most of the Hilbert space. The latter property leads to a possible quantum avoidance of the singularity ("cosmological bounce"), and suggests imposing the boundary condition that the wavefunction of the Universe vanish when the volume of space tends to zero. The space of solutions is a mixture of "discrete-spectrum states" (explicitely given) and of continuous-spectrum states (parametrized by arbitrary functions entering some initial-value problem). The predominantly negative values of the squared-mass term lead to a "bottle effect" between small and large volume-Universes and to a possible reduction of the continuous spectrum to a discrete spectrum of quantum states looking like excited versions of the Planckian-size Universes described by the discrete states at fermionic levels NF=0 and 1.

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arXiv2014

Two-body gravitational spin-orbit interaction at linear order in the mass ratio

We analytically compute, to linear order in the mass-ratio, the "geodetic" spin precession frequency of a small spinning body orbiting a large (non-spinning) body to the eight-and-a-half post-Newtonian order, thereby extending previous analytical knowledge which was limited to the third post-Newtonian level. These results are obtained applying analytical gravitational self-force theory to the first-derivative level generalization of Detweiler's gauge-invariant redshift variable. We compare our analytic results with strong-field numerical data recently obtained by S.~R.~Dolan et al. [Phys.\ Rev.\ D {\bf 89}, 064011 (2014)]. Our new, high-post-Newtonian-order results capture the strong-field features exhibited by the numerical data. We argue that the spin-precession will diverge as $\approx -0.14/(1-3y)$ as the light-ring is approached. We transcribe our kinematical spin-precession results into a corresponding improved analytic knowledge of one of the two (gauge-invariant) effective gyro-gravitomagnetic ratios characterizing spin-orbit couplings within the effective-one-body formalism. We provide simple, accurate analytic fits both for spin-precession and the effective gyro-gravitomagnetic ratio. The latter fit predicts that the linear-in-mass-ratio correction to the gyro-gravitomagnetic ratio changes sign before reaching the light-ring. This strong-field prediction might be important for improving the analytic modeling of coalescing spinning binaries.

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arXiv2014

Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems

We complete the analytical determination, at the 4th post-Newtonian (4PN) approximation, of the conservative dynamics of gravitationally interacting two-point-mass systems. This completion is obtained by resolving the infra-red ambiguity which had blocked a previous 4PN calculation [P.Jaranowski and G.Schäfer, Phys. Rev. D 87, 081503(R) (2013)] by taking into account the 4PN breakdown of the usual near-zone expansion due to infinite-range tail-transported temporal correlations found long ago [L.Blanchet and T.Damour, Phys. Rev. D 37, 1410 (1988)]. This leads to a Poincaré-invariant 4PN-accurate effective action for two masses, which mixes instantaneous interaction terms (described by a usual Hamiltonian) with a (time-symmetric) nonlocal-in-time interaction.

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arXiv2014

Analytic determination of the eight-and-a-half post-Newtonian self-force contributions to the two-body gravitational interaction potential

We {\it analytically} compute, to the eight-and-a-half post-Newtonian order, and to linear order in the mass ratio, the radial potential describing (within the effective one-body formalism) the gravitational interaction of two bodies, thereby extending previous analytic results. These results are obtained by applying analytical gravitational self-force theory (for a particle in circular orbit around a Schwarzschild black hole) to Detweiler's gauge-invariant redshift variable. We emphasize the increase in \lq\lq transcendentality" of the numbers entering the post-Newtonian expansion coefficients as the order increases, in particular we note the appearance of $ζ(3)$ (as well as the square of Euler's constant $γ$) starting at the seventh post-Newtonian order. We study the convergence of the post-Newtonian expansion as the expansion parameter $u=GM/(c^2r)$ leaves the weak-field domain $u\ll 1$ to enter the strong field domain $u=O(1)$.

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arXiv2014

Strong-Field Scattering of Two Black Holes: Numerics Versus Analytics

We probe the gravitational interaction of two black holes in the strong-field regime by computing the scattering angle $χ$ of hyperbolic-like, close binary-black-hole encounters as a function of the impact parameter. The fully general-relativistic result from numerical relativity is compared to two analytic approximations: post-Newtonian theory and the effective-one-body formalism. As the impact parameter decreases, so that black holes pass within a few times their Schwarzschild radii, we find that the post-Newtonian prediction becomes quite inaccurate, while the effective-one-body one keeps showing a good agreement with numerical results. Because we have explored a regime which is very different from the one considered so far with binaries in quasi-circular orbits, our results open a new avenue to improve analytic representations of the general-relativistic two-body Hamiltonian.

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arXiv2014

High-order post-Newtonian contributions to the two-body gravitational interaction potential from analytical gravitational self-force calculations

We extend the analytical determination of the main radial potential describing (within the effective one-body formalism) the gravitational interaction of two bodies beyond the 4th post-Newtonian approximation recently obtained by us. This extension is done to linear order in the mass ratio by applying analytical gravitational self-force theory (for a particle in circular orbit around a Schwarzschild black hole) to Detweiler's gauge-invariant redshift variable. By using the version of black hole perturbation theory developed by Mano, Suzuki and Takasugi, we have pushed the analytical determination of the (linear in mass ratio) radial potential to the 6th post-Newtonian order (passing through 5 and 5.5 post-Newtonian terms). In principle, our analytical method can be extended to arbitrarily high post-Newtonian orders.

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arXiv2013

The general relativistic two body problem

The two-body problem in General Relativity has been the subject of many analytical investigations. After reviewing some of the methods used to tackle this problem (and, more generally, the N-body problem), we focus on a new, recently introduced approach to the motion and radiation of (comparable mass) binary systems: the Effective One Body (EOB) formalism. We review the basic elements of this formalism, and discuss some of its recent developments. Several recent comparisons between EOB predictions and Numerical Relativity (NR) simulations have shown the aptitude of the EOB formalism to provide accurate descriptions of the dynamics and radiation of various binary systems (comprising black holes or neutron stars) in regimes that are inaccessible to other analytical approaches (such as the last orbits and the merger of comparable mass black holes). In synergy with NR simulations, post-Newtonian (PN) theory and Gravitational Self-Force (GSF) computations, the EOB formalism is likely to provide an efficient way of computing the very many accurate template waveforms that are needed for Gravitational Wave (GW) data analysis purposes.

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arXiv2013

Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration

The Numerical-Relativity-Analytical-Relativity (NRAR) collaboration is a joint effort between members of the numerical relativity, analytical relativity and gravitational-wave data analysis communities. The goal of the NRAR collaboration is to produce numerical-relativity simulations of compact binaries and use them to develop accurate analytical templates for the LIGO/Virgo Collaboration to use in detecting gravitational-wave signals and extracting astrophysical information from them. We describe the results of the first stage of the NRAR project, which focused on producing an initial set of numerical waveforms from binary black holes with moderate mass ratios and spins, as well as one non-spinning binary configuration which has a mass ratio of 10. All of the numerical waveforms are analysed in a uniform and consistent manner, with numerical errors evaluated using an analysis code created by members of the NRAR collaboration. We compare previously-calibrated, non-precessing analytical waveforms, notably the effective-one-body (EOB) and phenomenological template families, to the newly-produced numerical waveforms. We find that when the binary's total mass is ~100-200 solar masses, current EOB and phenomenological models of spinning, non-precessing binary waveforms have overlaps above 99% (for advanced LIGO) with all of the non-precessing-binary numerical waveforms with mass ratios <= 4, when maximizing over binary parameters. This implies that the loss of event rate due to modelling error is below 3%. Moreover, the non-spinning EOB waveforms previously calibrated to five non-spinning waveforms with mass ratio smaller than 6 have overlaps above 99.7% with the numerical waveform with a mass ratio of 10, without even maximizing on the binary parameters.

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arXiv2013

Merger states and final states of black hole coalescences: a numerical-relativity-assisted effective-one-body approach

We study to what extent the effective-one-body description of the dynamical state of a nonspinning, coalescing binary black hole (considered either at merger, or after ringdown) agrees with numerical relativity results. This comparison uses estimates of the integrated losses of energy and angular momentum during ringdown, inferred from recent numerical-relativity data. We find that the values, predicted by the effective-one-body formalism, of the energy and angular momentum of the system agree at the per mil level with their numerical-relativity counterparts, both at merger and in the final state. This gives a new confirmation of the ability of effective-one-body theory to accurately describe the dynamics of binary black holes even in the strong-gravitational-field regime. Our work also provides predictions (and analytical fits) for the final mass and the final spin of coalescing black holes for all mass ratios

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arXiv2013

Quantum Supersymmetric Cosmology and its Hidden Kac-Moody Structure

We study the quantum dynamics of a supersymmetric squashed three-sphere by dimensionally reducing (to one timelike dimension) the action of D=4 simple supergravity for an SO(3)-homogeneous (Bianchi IX) cosmological model. The quantization of the homogeneous gravitino field leads to a 64-dimensional fermionic Hilbert space. The algebra of the supersymmetry constraints and of the Hamiltonian one is found to close. One finds that the quantum Hamiltonian is built from operators that generate a 64-dimensional representation of the (infinite-dimensional) maximally compact sub-algebra of the rank-3 hyperbolic Kac-Moody algebra AE_3. Some exponentials of these operators generate a spinorial extension of the Weyl group of AE_3 which describe (in the small wavelength limit) the chaotic quantum evolution of the universe near the cosmological singularity.

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arXiv2013

Analytical determination of the two-body gravitational interaction potential at the 4th post-Newtonian approximation

We complete the analytical determination, at the 4th post-Newtonian approximation, of the main radial potential describing the gravitational interaction of two bodies within the effective one-body formalism. The (non logarithmic) coefficient a_5 (nu) measuring this 4th post-Newtonian interaction potential is found to be linear in the symmetric mass ratio nu. Its nu-independent part a_5 (0) is obtained by an analytical gravitational self-force calculation that unambiguously resolves the formal infrared divergencies which currently impede its direct post-Newtonian calculation. Its nu-linear part a_5 (nu) - a_5 (0) is deduced from recent results of Jaranowski and Schäfer, and is found to be significantly negative.

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arXiv2013

Improved effective-one-body description of coalescing nonspinning black-hole binaries and its numerical-relativity completion

We improve the effective-one-body (EOB) description of nonspinning coalescing black hole binaries by incorporating several recent analytical advances, notably: (i) logarithmic contributions to the conservative dynamics; (ii) resummed horizon-absorption contribution to the orbital angular momentum loss; and (iii) a specific radial component of the radiation reaction force implied by consistency with the azimuthal one. We then complete this analytically improved EOB model by comparing it to accurate numerical relativity (NR) simulations performed by the Caltech-Cornell-CITA group for mass ratios $q=(1,2,3,4,6)$. In particular, the comparison to NR data allows us to determine with high-accuracy ($\sim 10^{-4}$) the value of the main EOB radial potential: $A(u;\,ν)$, where $u=GM/(R c^2)$ is the inter-body gravitational potential and $ν=q/(q+1)^2$ is the symmetric mass ratio. We introduce a new technique for extracting from NR data an intrinsic measure of the phase evolution, ($Q_ω(ω)$ diagnostics). Aligning the NR-completed EOB quadrupolar waveform and the NR one at low frequencies, we find that they keep agreeing (in phase and amplitude) within the NR uncertainties throughout the evolution for all mass ratios considered. We also find good agreement for several subdominant multipoles without having to introduce and tune any extra parameters.

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arXiv2012

The General Relativistic Two Body Problem and the Effective One Body Formalism

A new analytical approach to the motion and radiation of (comparable mass) binary systems has been introduced in 1999 under the name of Effective One Body (EOB) formalism. We review the basic elements of this formalism, and discuss some of its recent developments. Several recent comparisons between EOB predictions and Numerical Relativity (NR) simulations have shown the aptitude of the EOB formalism to provide accurate descriptions of the dynamics and radiation of various binary systems (comprising black holes or neutron stars) in regimes that are inaccessible to other analytical approaches (such as the last orbits and the merger of comparable mass black holes). In synergy with NR simulations, post-Newtonian (PN) theory and Gravitational Self-Force (GSF) computations, the EOB formalism is likely to provide an efficient way of computing the very many accurate template waveforms that are needed for Gravitational Wave (GW) data analysis purposes.

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