arXiv subjects

Thibault Damour

Publications and source records attributed to Thibault Damour.

At least 37 records · Page 2Linked to original sources

arXiv2023

Double copy, Kerr-Schild gauges and the Effective-One-Body formalism

We look for a classical double copy structure between gravity and electrodynamics by connecting the descriptions of the scattering of two point masses, and of two point charges, in terms of perturbative (post-Minkowskian or post-Lorentzian) expansions. We do so by recasting available analytical information within the effective-one-body formalism using Kerr-Schild gauges in both cases. Working at the third perturbative level, we find that the usual linear relation (holding in the probe limit) between the dimensionless electric potential, $\tildeϕ= \frac{G M}{e_1 e_2} ϕ^{\rm el}$, and the Schwarzschildlike gravitational one, $Φ^{\rm grav}$, is deformed, in the comparable-mass, comparable-charge, case, into a nonlinear relation which becomes universal in the high energy limit: $Φ^{\rm grav}= 2\tildeϕ-5\tildeϕ^2 + 18\tildeϕ^3$.

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arXiv2023

Strong-field scattering of two spinning black holes: Numerical Relativity versus post-Minkowskian gravity

Highly accurate models of the gravitational-wave signal from coalescing compact binaries are built by completing analytical computations of the binary dynamics with non-perturbative information from numerical relativity (NR) simulations. In this paper we present four sets of NR simulations of equal-mass black hole binaries that undergo strong-field scattering: (i) we reproduce and extend the nonspinning simulations first presented in [Damour \textit{et al.}, Phys.Rev.D 89 (2014) 8, 081503], (ii) we compute two suites of nonspinning simulations at higher energies, probing stronger field interactions, (iii) we present a series of \textit{spinning} simulations including, for the first time, unequal-spin configurations. When comparing the NR scattering angles to analytical predictions based on state-of-the-art post-Minkowskian (PM) calculations, we find that PM-expanded scattering angles show poor convergence towards NR data. By contrast, a resummed computation of scattering angles via a spin-dependent, radiation-reacted, effective-one-body potential shows excellent agreement for both nonspinning and spinning configurations.

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arXiv2023

Faithful effective-one-body waveform of small-mass-ratio coalescing black hole binaries: the eccentric, nonspinning, case

We present a new effective-one-body (EOB) waveform for eccentric, nonspinning, binaries in the extreme mass ratio limit, with initial eccentricities up to $0.95$. The EOB analytical waveform, that includes noncircular corrections up to second post-Newtonian order, is completed by a phenomenological ringdown model that is informed by Regge-Wheeler-Zerilli (RWZ) type waveforms generated by a point-particle source. This model notably includes the beating between positive and negative frequency quasi-normal-modes (QNMs). We analyze various prescriptions to faithfully complete the analytical EOB waveform in the transition from plunge to merger. In particular, we systematically explore the effect of: (i) the generic Newtonian prefactor; (ii) next-to-quasi-circular (NQC) corrections to amplitude and phase; (iii) the point were NQC corrections are determined; (iv) the ringdown attachment point. This yields EOB/RWZ quadrupolar phase differences through merger and ringdown $\lesssim 0.01$~rad for the quasi-circular case and $\lesssim 0.05$~rad for the eccentric case. Higher modes are also modeled up to the $\ell=m=5$ multipole. We finally discuss the excitation of the QNMs and present a heuristic model to motivate it in correlation with the presence of a point-particle source.

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arXiv2023

Strong-field scattering of two black holes: Numerical Relativity meets Post-Minkowskian gravity

We compare numerical relativity (NR) data on the scattering of equal-mass, non-spinning binary black holes to various analytical predictions based on post-Minkowskian (PM) results. While the usual sequence of PM-expanded scattering angles shows a rather poor convergence towards NR data, we find that a reformulation of PM information in terms of Effective-One-Body radial potentials leads to remarkable agreement with NR data, especially when using the radiation-reacted 4PM information. Using Firsov's inversion formula we directly extract, for the first time, from NR simulations a (radiation-reacted) gravitational potential describing the scattering of equal-mass, non-spinning binary black holes. We urge the NR community to compute more sequences of scattering simulations, so as to extend this knowledge to a wider region of parameter space.

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arXiv2022

Radiation-reaction and angular momentum loss at the second Post-Minkowskian order

We compute the variation of the Fokker-Wheeler-Feynman total linear and angular momentum of a gravitationally interacting binary system under the second post-Minkowskian retarded dynamics. The resulting $O(G^2)$ equations-of-motion-based, total change in the system's angular momentum is found to agree with existing computations that assumed balance with angular momentum fluxes in the radiation zone.

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arXiv2022

Radiated momentum and radiation-reaction in gravitational two-body scattering including time-asymmetric effects

We compute to high post-Newtonian accuracy the 4-momentum (linear momentum, and energy), radiated as gravitational waves in a two-body system undergoing gravitational scattering. We include, for the first time, all the relevant {\it time-asymmetric} effects that arise when consistently going three post Newtonian orders beyond the leading post Newtonian order. We find that the inclusion of time-asymmetric radiative effects (both in tails and in the radiation-reacted hyperbolic motion) is crucial to ensure the mass-polynomiality of the post-Minkowskian expansion ($G$ expansion) of the radiated 4-momentum. Imposing the mass-polynomiality of the corresponding individual impulses determines the conservativelike radiative contributions at the fourth post-Minkowskian order, and strongly constrains them at the fifth post-Minkowskian order.

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arXiv2022

Result of the MICROSCOPE Weak Equivalence Principle test

The space mission MICROSCOPE dedicated to the test of the Equivalence Principle (EP) operated from April 25, 2016 until the deactivation of the satellite on October 16, 2018. In this analysis we compare the free-fall accelerations ($a_{\rm A}$ and $a_{\rm B}$) of two test masses in terms of the Eötvös parameter $η({\rm{A, B}}) = 2 \frac{a_{\rm A}- a_{\rm B}}{a_{\rm A}+ a_{\rm B}}$. No EP violation has been detected for two test masses, made from platinum and titanium alloys, in a sequence of 19 segments lasting from 13 to 198 hours down to the limit of the statistical error which is smaller than $10^{-14}$ for $ η({\rm{Ti, Pt}})$. Accumulating data from all segments leads to $η({\rm{Ti, Pt}}) =[-1.5\pm{}2.3{\rm (stat)}\pm{}1.5{\rm (syst)}] \times{}10^{-15}$ showing no EP violation at the level of $2.7\times{}10^{-15}$ if we combine stochastic and systematic errors quadratically. This represents an improvement of almost two orders of magnitude with respect to the previous best such test performed by the Eöt-Wash group. The reliability of this limit has been verified by comparing the free falls of two test masses of the same composition (platinum) leading to a null Eötvös parameter with a statistical uncertainty of $1.1\times{}10^{-15}$.

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arXiv2022

MICROSCOPE mission: final results of the test of the Equivalence Principle

The MICROSCOPE mission was designed to test the Weak Equivalence Principle (WEP), stating the equality between the inertial and the gravitational masses, with a precision of $10^{-15}$ in terms of the Eötvös ratio $η$. Its experimental test consisted of comparing the accelerations undergone by two collocated test masses of different compositions as they orbited the Earth, by measuring the electrostatic forces required to keep them in equilibrium. This was done with ultra-sensitive differential electrostatic accelerometers onboard a drag-free satellite. The mission lasted two and a half years, cumulating five-months-worth of science free-fall data, two thirds with a pair of test masses of different compositions -- Titanium and Platinum alloys -- and the last third with a reference pair of test masses of the same composition -- Platinum. We summarize the data analysis, with an emphasis on the characterization of the systematic uncertainties due to thermal instabilities and on the correction of short-lived events which could mimic a WEP violation signal. We found no violation of the WEP, with the Eötvös parameter of the Titanium and Platinum pair constrained to $η({\rm Ti, Pt})~=~ [-1.5 \pm 2.3~{\rm (stat)} \pm 1.5~{\rm (syst)}]~\times 10^{-15}$ at $1σ$ in statistical errors.

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arXiv2022

Hidden Kac-Moody Structures in the Fermionic Sector of Five-Dimensional Supergravity

We study the supersymmetric quantum dynamics of the cosmological models obtained by reducing $D=5$ supergravity to one timelike dimension. This consistent truncation has fourteen bosonic degrees of freedom, while the quantization of the homogeneous gravitino field leads to a $2^{16}$--dimensional fermionic Hilbert space. We construct a consistent quantization of the model in which the wave function of the Universe is a $2^{16}$--component spinor %\textcolor{red}{of Spin(24,8)} depending on fourteen continuous coordinates, which satisfies eight Dirac-like wave equations (supersymmetry constraints) and one Klein-Gordon-like equation (Hamiltonian constraint). The fermionic part of the quantum Hamiltonian is built from operators that generate a $2^{16}$-dimensional representation of the (infinite-dimensional) maximally compact sub-algebra $K(G_2^{++})$ of the rank-4 hyperbolic Kac--Moody algebra $G_2^{++}$. The (quartic-in-fermions) squared-mass term $\widehat μ^2$ entering the Klein-Gordon-like equation has several remarkable properties: (i) it commutes with the generators of $K(G_2^{++})$; and (ii) it is a quadratic polynomial in the fermion number $N_F \sim \overlineΨΨ$, and a symplectic fermion bilinear $C_F \sim ΨCΨ$. Some aspects of the structure of the solutions of our model are discussed, and notably the Kac-Moody meaning of the operators describing the reflection of the wave function on the fermion-dependent potential walls ("quantum fermionic Kac-Moody billiard").

hep-th↗

arXiv2021

Radiative contributions to gravitational scattering

The linear-order effects of radiation-reaction on the classical scattering of two point masses, in General Relativity, are derived by a variation-of-constants method. Explicit expressions for the radiation-reaction contributions to the changes of 4-momentum during scattering are given to linear order in the radiative losses of energy, linear-momentum and angular momentum. The polynomial dependence on the masses of the 4-momentum changes is shown to lead to non-trivial identities relating the various radiative losses. At order $G^3$ our results lead to a streamlined classical derivation of results recently derived within a quantum approach. At order $G^4$ we compute the needed radiative losses to next-to-next-to-leading-order in the post-Newtonian expansion, thereby reaching the absolute fourth and a half post-Newtonian level of accuracy in the 4-momentum changes. We also provide explicit expressions, at the absolute sixth post-Newtonian accuracy, for the radiation-graviton contribution to {\it conservative} $O(G^4)$ scattering. At orders $G^5$ and $G^6$ we derive explicit theoretical expressions for the last two hitherto undetermined parameters describing the fifth-post-Newtonian dynamics. Our results at the fifth-post-Newtonian level confirm results of [Nucl. Phys. B \textbf{965}, 115352 (2021)] but exhibit some disagreements with results of [Phys. Rev. D \textbf{101}, 064033 (2020)].

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arXiv2021

Dynamical systems with benign ghosts

We consider finite and infinite-dimensional ghost-ridden dynamical systems whose Hamiltonians involve non positive definite kinetic terms. We point out the existence of three classes of such systems where the ghosts are benign, i.e. systems whose evolution is unlimited in time:(i) systems obtained from the variation of bounded-motion systems; (ii) systems describing motions over certain Lorentzian manifolds and (iii) higher-derivative models related to certain modified Korteweg--de Vries equations.

hep-th↗

arXiv2020

Gravitational scattering at the seventh order in $G$: nonlocal contribution at the sixth post-Newtonian accuracy

A recently introduced approach to the classical gravitational dynamics of binary systems involves intricate integrals (linked to a combination of nonlocal-in-time interactions with iterated $\frac1r$-potential scattering) which have so far resisted attempts at their analytical evaluation. By using computing techniques developed for the evaluation of multi-loop Feynman integrals (notably Harmonic Polylogarithms and Mellin transform) we show how to analytically compute all the integrals entering the nonlocal-in-time contribution to the classical scattering angle at the sixth post-Newtonian accuracy, and at the seventh order in Newton's constant, $G$ (corresponding to six-loop graphs in the diagrammatic representation of the classical scattering angle).

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arXiv2020

Radiative contribution to classical gravitational scattering at the third order in $G$

Working within the post-Minkowskian approach to General Relativity, we prove that the radiation-reaction to the emission of gravitational waves during the large-impact-parameter scattering of two (classical) point masses modifies the conservative scattering angle by an additional contribution of order $G^3$ which involves a high-energy (or massless) logarithmic divergence of opposite sign to the one contained in the third-post-Minkowskian result of Bern et al. [Phys. Rev. Lett. {\bf 122}, 201603 (2019)]. The high-energy limit of the resulting radiation-reaction-corrected (classical) scattering angle is finite, and is found to agree with the one following from the (quantum) eikonal-phase result of Amati, Ciafaloni and Veneziano [ Nucl. Phys. B {\bf 347}, 550 (1990)].

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arXiv2020

Gravitational dynamics at $O(G^6)$: perturbative gravitational scattering meets experimental mathematics

A recently introduced approach to the gravitational dynamics of binary systems involves intricate integrals, linked to nonlocal-in-time interactions arising at the 5-loop level of classical gravitational scattering. We complete the analytical evaluation of classical gravitational scattering at the sixth order in Newton's constant, $G$, and at the sixth post-Newtonian accuracy. We use computing techniques developed for the evaluation of multi-loop Feynman integrals to obtain our results in two ways: high-precision arithmetic, yielding reconstructed analytic expressions, and direct integration {\it via} Harmonic Polylogarithms. The analytic expression of the tail contribution to the scattering involve transcendental constants up to weight four.

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arXiv2020

Sixth post-Newtonian nonlocal-in-time dynamics of binary systems

We complete our previous derivation, at the sixth post-Newtonian (6PN) accuracy, of the local-in-time dynamics of a gravitationally interacting two-body system by giving two gauge-invariant characterizations of its complementary nonlocal-in-time dynamics. On the one hand, we compute the nonlocal part of the scattering angle for hyberboliclike motions; and, on the other hand, we compute the nonlocal part of the averaged (Delaunay) Hamiltonian for ellipticlike motions. The former is computed as a large-angular-momentum expansion (given here to next-to-next-to-leading order), while the latter is given as a small-eccentricity expansion (given here to the tenth order). We note the appearance of $ζ(3)$ in the nonlocal part of the scattering angle. The averaged Hamiltonian for ellipticlike motions then yields two more gauge-invariant observables: the energy and the periastron precession as functions of orbital frequencies. We point out the existence of a hidden simplicity in the mass-ratio dependence of the gravitational-wave energy loss of a two-body system.

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arXiv2020

Classical and quantum scattering in post-Minkowskian gravity

New structural properties of post-Minkowskian (PM) gravity are derived, notably within its effective one body (EOB) formulation. Our results concern both the mass dependence, and the high-energy behavior, of the classical scattering angle. We generalize our previous work by deriving, up to the fourth post-Minkowskian (4PM) level included, the explicit links between the scattering angle and the two types of potentials entering the Hamiltonian description of PM dynamics within EOB theory. We compute the scattering amplitude derived from quantizing the third post-Minkowskian (3PM) EOB radial potential (including the contributions coming from the Born iterations), and point out various subtleties in the relation between perturbative amplitudes and classical dynamics. We highlight an apparent tension between the classical 3PM dynamics derived by Bern et al. [Phys. Rev. Lett. 122, 201603 (2019)], and previous high-energy self-force results [Phys. Rev. D 86, 104041 (2012)], and propose several possible resolutions of this tension. We point out that linear-in-mass-ratio self-force computations can give access to the exact 3PM and 4PM dynamics.

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arXiv2020

Black holes in torsion bigravity

We study spherically symmetric black hole solutions in a four-parameter Einstein-Cartan-type class of theories, called "torsion bigravity". These theories offer a geometric framework (with a metric and an independent torsionfull connection) for a modification of Einstein's theory that has the same spectrum as bimetric gravity models. In addition to an Einsteinlike massless spin-2 excitation, there is a massive spin-2 one (of range $κ^{-1}$) coming from the torsion sector, rather than from a second metric. We prove the existence of three broad classes of spherically-symmetric black hole solutions in torsion bigravity. First, the Schwarzschild solution defines an asymptotically-flat torsionless black hole for all values of the parameters. [And we prove that one cannot deform a Schwarzschild solution, at the linearized level, by adding an infinitesimal torsion hair.] Second, when considering finite values of the range, we find that there exist non-asymptotically-flat torsion-hairy black holes in a large domain of parameter space. Third, we find that, in the limit of infinite range, there exists a two-parameter family of asymptotically flat torsion-hairy black holes. The latter black hole solutions give an interesting example of non-Einsteinian (but still purely geometric) black hole structures which might be astrophysically relevant when considering a range of cosmological size.

gr-qc↗

arXiv2020

Sixth post-Newtonian local-in-time dynamics of binary systems

Using a recently introduced method [Phys.\ Rev.\ Lett.\ {\bf 123}, 231104 (2019)], which splits the conservative dynamics of gravitationally interacting binary systems into a non-local-in-time part and a local-in-time one, we compute the local part of the dynamics at the sixth post-Newtonian (6PN) accuracy. Our strategy combines several theoretical formalisms: post-Newtonian, post-Minkowskian, multipolar-post-Minkowskian, effective-field-theory, gravitational self-force, effective one-body, and Delaunay averaging. The full functional structure of the local 6PN Hamiltonian (which involves 151 numerical coefficients) is derived, but contains four undetermined numerical coefficients. Our 6PN-accurate results are complete at orders $G^3$ and $G^4$, and the derived $O(G^3)$ scattering angle agrees, within our 6PN accuracy, with the computation of [Phys.\ Rev.\ Lett.\ {\bf 122}, no. 20, 201603 (2019)]. All our results are expressed in several different gauge-invariant ways. We highlight, and make a crucial use of, several aspects of the hidden simplicity of the mass-ratio dependence of the two-body dynamics.

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