arXiv subjects

Thibault Damour

Publications and source records attributed to Thibault Damour.

At least 127 records · Page 7Linked to original sources

arXiv2009

Effective One Body description of tidal effects in inspiralling compact binaries

The late part of the gravitational wave signal of binary neutron star inspirals can in principle yield crucial information on the nuclear equation of state via its dependence on relativistic tidal parameters. In the hope of analytically describing the gravitational wave phasing during the late inspiral (essentially up to contact) we propose an extension of the effective one body (EOB) formalism which includes tidal effects. We compare the prediction of this tidal-EOB formalism to recently computed nonconformally flat quasi-equilibrium circular sequences of binary neutron star systems. Our analysis suggests the importance of higher-order (post-Newtonian) corrections to tidal effects, even beyond the first post-Newtonian order, and their tendency to {\it significantly} increase the ``effective tidal polarizability'' of neutron stars. We compare the EOB predictions to some recently advocated, nonresummed, post-Newtonian based (``Taylor-T4'') description of the phasing of inspiralling systems. This comparison shows the strong sensitivity of the late-inspiral phasing to the choice of the analytical model, but raises the hope that a sufficiently accurate numerical--relativity--``calibrated'' EOB model might give us a reliable handle on the nuclear equation of state

gr-qc↗

arXiv2009

Gravitational Self Force in a Schwarzschild Background and the Effective One Body Formalism

We discuss various ways in which the computation of conservative Gravitational Self Force (GSF) effects on a point mass moving in a Schwarzschild background can inform us about the basic building blocks of the Effective One-Body (EOB) Hamiltonian. We display the information which can be extracted from the recently published GSF calculation of the first-GSF-order shift of the orbital frequency of the last stable circular orbit, and we combine this information with the one recently obtained by comparing the EOB formalism to high-accuracy numerical relativity (NR) data on coalescing binary black holes. The information coming from GSF data helps to break the degeneracy (among some EOB parameters) which was left after using comparable-mass NR data to constrain the EOB formalism. We suggest various ways of obtaining more information from GSF computations: either by studying eccentric orbits, or by focussing on a special zero-binding zoom-whirl orbit. We show that logarithmic terms start entering the post-Newtonian expansions of various (EOB and GSF) functions at the fourth post-Newtonian (4PN) level, and we analytically compute the first logarithm entering a certain, gauge-invariant "redshift" GSF function (defined along the sequence of circular orbits).

gr-qc↗

arXiv2009

On the gravitational polarizability of black holes

The gravitational polarizability properties of black holes are compared and contrasted with their electromagnetic polarizability properties. The "shape" or "height" multipolar Love numbers h_l of a black hole are defined and computed. They are then compared to their electromagnetic analogs h_l^{EM}. The Love numbers h_l give the height of the l-th multipolar "tidal bulge" raised on the horizon of a black hole by faraway masses. We also discuss the shape of the tidal bulge raised by a test mass m, in the limit where m gets very close to the horizon.

gr-qc↗

arXiv2009

The Equivalence Principle and the Constants of Nature

We briefly review the various contexts within which one might address the issue of ``why'' the dimensionless constants of Nature have the particular values that they are observed to have. Both the general historical trend, in physics, of replacing a-priori-given, absolute structures by dynamical entities, and anthropic considerations, suggest that coupling ``constants'' have a dynamical nature. This hints at the existence of observable violations of the Equivalence Principle at some level, and motivates the need for improved tests of the Equivalence Principle.

gr-qc↗

arXiv2009

The Effective One Body description of the Two-Body problem

The Effective One Body (EOB) formalism is an analytical approach which aims at providing an accurate description of the motion and radiation of coalescing binary black holes with arbitrary mass ratio. We review the basic elements of this formalism and discuss its aptitude at providing accurate template waveforms to be used for gravitational wave data analysis purposes.

gr-qc↗

arXiv2009

An improved analytical description of inspiralling and coalescing black-hole binaries

We present an analytical formalism, within the Effective-One-Body framework, which predicts gravitational-wave signals from inspiralling and coalescing black-hole binaries that agree, within numerical errors, with the results of the currently most accurate numerical relativity simulations for several different mass ratios. In the equal-mass case, the gravitational wave energy flux predicted by our formalism agrees, within numerical errors, with the most accurate numerical-relativity energy flux. We think that our formalism opens a realistic possibility of constructing a sufficiently accurate, large bank of gravitational wave templates, as needed both for detection and data analysis of (non spinning) coalescing binary black holes.

gr-qc↗

arXiv2009

Improved resummation of post-Newtonian multipolar waveforms from circularized compact binaries

We improve and generalize a resummation method of post-Newtonian multipolar waveforms from circular compact binaries introduced in Refs. \cite{Damour:2007xr,Damour:2007yf}. One of the characteristic features of this resummation method is to replace the usual {\it additive} decomposition of the standard post-Newtonian approach by a {\it multiplicative} decomposition of the complex multipolar waveform $h_{\lm}$ into several (physically motivated) factors: (i) the "Newtonian" waveform, (ii) a relativistic correction coming from an "effective source", (iii) leading-order tail effects linked to propagation on a Schwarzschild background, (iv) a residual tail dephasing, and (v) residual relativistic amplitude corrections $f_{\lm}$. We explore here a new route for resumming $f_{\lm}$ based on replacing it by its $\ell$-th root: $ρ_{\lm}=f_{\lm}^{1/\ell}$. In the extreme-mass-ratio case, this resummation procedure results in a much better agreement between analytical and numerical waveforms than when using standard post-Newtonian approximants. We then show that our best approximants behave in a robust and continuous manner as we "deform" them by increasing the symmetric mass ratio $ν\equiv m_1 m_2/(m_1+m_2)^2$ from 0 (extreme-mass-ratio case) to 1/4 (equal-mass case). The present paper also completes our knowledge of the first post-Newtonian corrections to multipole moments by computing ready-to-use explicit expressions for the first post-Newtonian contributions to the odd-parity (current) multipoles.

gr-qc↗

arXiv2008

Faithful Effective-One-Body waveforms of equal-mass coalescing black-hole binaries

We continue the program of constructing, within the Effective-One-Body (EOB) approach, high-accuracy analytic waveforms describing the signal emitted by inspiralling and coalescing black hole binaries. Here, we compare a recently derived, resummed 3 PN-accurate EOB quadrupolar waveform to the results of a numerical simulation of the inspiral and merger of an equal-mass black hole binary. We find a remarkable agreement, both in phase and in amplitude, with a maximal dephasing which can be reduced below $\pm 0.005$ gravitational-wave (GW) cycles over 12 GW cycles corresponding to the end of the inspiral, the plunge, the merger and the beginning of the ringdown. This level of agreement is shown for two different values of the effective 4 PN parameter a_5, and for corresponding, appropriately "flexed" values of the radiation-reaction resummation parameter v_pole. In addition, our resummed EOB amplitude agrees to better than the 1% level with the numerical-relativity one up to the late inspiral. These results, together with other recent work on the EOB-numerical-relativity comparison, confirm the ability of the EOB formalism to faithfully capture the general relativistic waveforms.

gr-qc↗

arXiv2008

Accurate Effective-One-Body waveforms of inspiralling and coalescing black-hole binaries

The Effective-One-Body (EOB) formalism contains several flexibility parameters, notably $a_5$, $\vp$ and $\a$. We show here how to jointly constrain the values of these parameters by simultaneously best-fitting the EOB waveform to two, independent, numerical relativity (NR) simulations of inspiralling and/or coalescing binary black hole systems: published Caltech-Cornell {\it inspiral} data (considered for gravitational wave frequencies $Mω\leq 0.1$) on one side, and newly computed {\it coalescence} data on the other side. The resulting, approximately unique, "best-fit" EOB waveform is then shown to exhibit excellent agreement with NR coalescence data for several mass ratios. The dephasing between this best-fit EOB waveform and published Caltech-Cornell inspiral data is found to vary between -0.0014 and +0.0008 radians over a time span of $\sim 2464M$ up to gravitational wave frequency $Mω= 0.1$, and between +0.0013 and -0.0185 over a time span of 96M after $Mω=0.1$ up to $Mω=0.1565$. The dephasings between EOB and the new coalescence data are found to be smaller than: (i) $\pm 0.025$ radians over a time span of 730M (11 cycles) up to merger, in the equal mass case, and (ii) $\pm 0.05$ radians over a time span of about 950M (17 cycles) up to merger in the 2:1 mass-ratio case. These new results corroborate the aptitude of the EOB formalism to provide accurate representations of general relativistic waveforms, which are needed by currently operating gravitational wave detectors.

gr-qc↗

arXiv2008

What is missing from Minkowski's "Raum und Zeit" lecture

This contribution tries to highlight the importance of Minkowski's ``Raum und Zeit'' lecture in a ``negative'' way, where {\it negative} is taken in the photographic sense of reversing lights and shades. Indeed, we focus on the ``shades'' of Minkowski's text, i.e. what is missing, or misunderstood. In particular, we focus on two issues: (i) why are Poincaré's pioneering contributions to four-dimensional geometry not quoted by Minkowski (while he abundantly quoted them a few months before the Cologne lecture)?, and (ii) did Minkowski fully grasp the physical (and existential) meaning of ``time'' within spacetime? We think that this ``negative'' approach (and the contrast between Poincaré's and Minkowski's attitudes towards physics) allows one to better grasp the boldness of the {\it revolutionary} step taken by Minkowski in his Cologne lecture.

physics.hist-ph↗

arXiv2008

Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling

A Hamiltonian formulation is given for the gravitational dynamics of two spinning compact bodies to next-to-leading order ($G/c^4$ and $G^2/c^4$) in the spin-orbit interaction. We use a novel approach (valid to linear order in the spins), which starts from the second-post-Newtonian metric (in ADM coordinates) generated by two spinless bodies, and computes the next-to-leading order precession, in this metric, of suitably redefined ``constant-magnitude'' 3-dimensional spin vectors ${\bf S}_1$, ${\bf S}_2$. We prove the Poincaré invariance of our Hamiltonian by explicitly constructing ten phase-space generators realizing the Poincaré algebra. A remarkable feature of our approach is that it allows one to derive the {\it orbital} equations of motion of spinning binaries to next-to-leading order in spin-orbit coupling without having to solve Einstein's field equations with a spin-dependent stress tensor. We show that our Hamiltonian (orbital and spin) dynamics is equivalent to the dynamics recently obtained by Faye, Blanchet, and Buonanno, by solving Einstein's equations in harmonic coordinates.

gr-qc↗

arXiv2008

Dimensional regularization of the gravitational interaction of point masses in the ADM formalism

The ADM formalism for two-point-mass systems in $d$ space dimensions is sketched. It is pointed out that the regularization ambiguities of the 3rd post-Newtonian ADM Hamiltonian considered directly in $d=3$ space dimensions can be cured by dimensional continuation (to complex $d$'s), which leads to a finite and unique Hamiltonian as $d\to3$. Some so far unpublished details of the dimensional-continuation computation of the 3rd post-Newtonian two-point-mass ADM Hamiltonian are presented.

gr-qc↗

arXiv2008

Effective one body approach to the dynamics of two spinning black holes with next-to-leading order spin-orbit coupling

Using a recent, novel Hamiltonian formulation of the gravitational interaction of spinning binaries, we extend the Effective One Body (EOB) description of the dynamics of two spinning black holes to next-to-leading order (NLO) in the spin-orbit interaction. The spin-dependent EOB Hamiltonian is constructed from four main ingredients: (i) a transformation between the ``effective'' Hamiltonian and the ``real'' one, (ii) a generalized effective Hamilton-Jacobi equation involving higher powers of the momenta, (iii) a Kerr-type effective metric (with Padé-resummed coefficients) which depends on the choice of some basic ``effective spin vector'' $\bf{S}_{\rm eff}$, and which is deformed by comparable-mass effects, and (iv) an additional effective spin-orbit interaction term involving another spin vector $\bsigma$. As a first application of the new, NLO spin-dependent EOB Hamiltonian, we compute the binding energy of circular orbits (for parallel spins) as a function of the orbital frequency, and of the spin parameters. We also study the characteristics of the last stable circular orbit: binding energy, orbital frequency, and the corresponding dimensionless spin parameter $\hat{a}_{\rm LSO}\equiv c J_{\rm LSO}/\boldsymbol(G(H_{\rm LSO}/c^2)^2\boldsymbol)$. We find that the inclusion of NLO spin-orbit terms has a significant ``moderating'' effect on the dynamical characteristics of the circular orbits for large and parallel spins.

gr-qc↗

arXiv2008

String theory, gravity and experiment

The aim of these lectures is to give an introduction to several topics which lie at the intersection of string theory, gravity theory and gravity phenomenology. One successively reviews: (i) the "membrane" approach to the dissipative dynamics of classical black holes, (ii) the current experimental tests of gravity, and their theoretical interpretation, (iii) some aspects of the string-inspired phenomenology of the gravitational sector, and (iv) some possibilities for observing string-related signals in cosmology (including a discussion of gravitational wave signals from cosmic superstrings).

hep-th↗

arXiv2008

Introductory lectures on the Effective One Body formalism

The Effective One Body (EOB) formalism is an analytical approach which aims at providing an accurate description of the motion and radiation of coalescing binary black holes. We present a brief review of the basic elements of this approach.

gr-qc↗

arXiv2007

Comparing Effective-One-Body gravitational waveforms to accurate numerical data

We continue the program of constructing, within the Effective-One-Body (EOB) approach, high accuracy, faithful analytic waveforms describing the gravitational wave signal emitted by inspiralling and coalescing binary black holes (BHs). We present the comparable-mass version of a new, resummed 3PN-accurate EOB quadrupolar waveform recently introduced in the small-mass-ratio limit. We compare the phase and the amplitude of this waveform to the recently published results of a high-accuracy numerical relativity (NR) simulation of 15 orbits of an inspiralling equal-mass binary BHs system performed by the Caltech-Cornell group. We find a remarkable agreement, both in phase and in amplitude, between the new EOB waveform and the published numerical data. More precisely: (i) in the gravitational wave (GW) frequency domain $Mω<0.08$ where the phase of one of the non-resummed ``Taylor approximant'' (T4) waveform matches well with the numerical relativity one, we find that the EOB phase fares as well, while (ii) for higher GW frequencies, $0.08<Mω\lesssim 0.14$, where the TaylorT4 approximant starts to significantly diverge from the NR phase, we show that the EOB phase continues to match well the NR one. We further propose various methods of tuning the two inspiral flexibility parameters, $a_5$ and $v_{\rm pole}$, of the EOB waveform so as to ``best fit'' EOB predictions to numerical data. We find that the maximal dephasing between EOB and NR can then be reduced below $10^{-3}$ GW cycles over the entire span (30 GW cycles) of the simulation. Our resummed EOB amplitude agrees much better with the NR one than any of the previously considered non-resummed, post-Newtonian one.

gr-qc↗

arXiv2007

Constraints on the variability of quark masses from nuclear binding

Based on recent work on nuclear binding, we update and extend the anthropic constraints on the light quark masses, with results that are more tightly constrained than previously obtained. We find that heavy nuclei would fall apart (because the attractive nuclear central potential becomes too weak) if the sum of the light quark masses m_u+m_d would exceed their physical values by 64% (at 95% confidence level). We summarize the anthropic constraints that follow from requiring the existence both of heavy atoms and of hydrogen. With the additional assumption that the quark Yukawa couplings do not vary, these constraints provide a remarkably tight anthropic window for the Higgs vacuum expectation value: 0.39 < v/v_physical < 1.64.

hep-ph↗

arXiv2007

Describing general cosmological singularities in Iwasawa variables

Belinskii, Khalatnikov, and Lifshitz (BKL) conjectured that the description of the asymptotic behavior of a generic solution of Einstein equations near a spacelike singularity could be drastically simplified by considering that the time derivatives of the metric asymptotically dominate (except at a sequence of instants, in the `chaotic case') over the spatial derivatives. We present a precise formulation of the BKL conjecture (in the chaotic case) that consists of basically three elements: (i) we parametrize the spatial metric $g_{ij}$ by means of \it{Iwasawa variables} $β^a, {\cal N}^a{}_i$); (ii) we define, at each spatial point, a (chaotic) \it{asymptotic evolution system} made of ordinary differential equations for the Iwasawa variables; and (iii) we characterize the exact Einstein solutions $β, {\cal{N}}$ whose asymptotic behavior is described by a solution $β_{[0]}, {\cal N}_{[0]}$ of the previous evolution system by means of a `\it{generalized Fuchsian system}' for the differenced variables $\bar β= β- β_{[0]}$, $\bar {\cal N} = {\cal N} - {\cal N}_{[0]}$, and by requiring that $\bar β$ and $\bar {\cal N}$ tend to zero on the singularity. We also show that, in spite of the apparently chaotic infinite succession of `Kasner epochs' near the singularity, there exists a well-defined \it{asymptotic geometrical structure} on the singularity : it is described by a \it{partially framed flag}. Our treatment encompasses Einstein-matter systems (comprising scalar and p-forms), and also shows how the use of Iwasawa variables can simplify the usual (`asymptotically velocity term dominated') description of non-chaotic systems.

gr-qc↗