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Thibault Damour

Publications and source records attributed to Thibault Damour.

At least 109 records · Page 6Linked to original sources
arXiv2012

Gravitational self-force and the effective-one-body formalism between the innermost stable circular orbit and the light ring

We compute the conservative piece of the gravitational self-force (GSF) acting on a particle of mass m_1 as it moves along an (unstable) circular geodesic orbit between the innermost stable circular orbit (ISCO) and the light ring of a Schwarzschild black hole of mass m_2>> m_1. More precisely, we construct the function h_{uu}(x) = h_{μν} u^μ u^ν (related to Detweiler's gauge-invariant "redshift" variable), where h_{μν} is the regularized metric perturbation in the Lorenz gauge, u^μ is the four-velocity of m_1, and x= [Gc^{-3}(m_1+m_2)Ω]^{2/3} is an invariant coordinate constructed from the orbital frequency Ω. In particular, we explore the behavior of h_{uu} just outside the "light ring" at x=1/3, where the circular orbit becomes null. Using the recently discovered link between h_{uu} and the piece a(u), linear in the symmetric mass ratio ν, of the main radial potential A(u,ν) of the Effective One Body (EOB) formalism, we compute a(u) over the entire domain 0<u<1/3. We find that a(u) diverges at the light-ring as ~0.25 (1-3u)^{-1/2}, explain the physical origin of this divergence, and discuss its consequences for the EOB formalism. We construct accurate global analytic fits for a(u), valid on the entire domain 0<u<1/3 (and possibly beyond), and give accurate numerical estimates of the values of a(u) and its first 3 derivatives at the ISCO, as well as the O(ν) shift in the ISCO frequency. In previous work we used GSF data on slightly eccentric orbits to compute a certain linear combination of a(u) and its first two derivatives, involving also the O(ν) piece \bar d(u) of a second EOB radial potential {\bar D}(u,ν). Combining these results with our present global analytic representation of a(u), we numerically compute {\bar d}(u)$ on the interval 0<u\leq 1/6.

gr-qc↗
arXiv2012

Gravitational radiation reaction along general orbits in the effective one-body formalism

We derive the gravitational radiation-reaction force modifying the Effective One Body (EOB) description of the conservative dynamics of binary systems. Our result is applicable to general orbits (elliptic or hyperbolic) and keeps terms of fractional second post-Newtonian order (but does not include tail effects). Our derivation of radiation-reaction is based on a new way of requiring energy and angular momentum balance. We give several applications of our results, notably the value of the (minimal) "Schott" contribution to the energy, the radial component of the radiation-reaction force, and the radiative contribution to the angle of scattering during hyperbolic encounters. We present also new results about the conservative relativistic dynamics of hyperbolic motions.

gr-qc↗
arXiv2012

Effective action approach to higher-order relativistic tidal interactions in binary systems and their effective one body description

The gravitational-wave signal from inspiralling neutron-star--neutron-star (or black-hole--neutron-star) binaries will be influenced by tidal coupling in the system. An important science goal in the gravitational-wave detection of these systems is to obtain information about the equation of state of neutron star matter via the measurement of the tidal polarizability parameters of neutron stars. To extract this piece of information will require to have accurate analytical descriptions of both the motion and the radiation of tidally interacting binaries. We improve the analytical description of the late inspiral dynamics by computing the next-to-next-to-leading order relativistic correction to the tidal interaction energy. Our calculation is based on an effective-action approach to tidal interactions, and on its transcription within the effective-one-body formalism. We find that second-order relativistic effects (quadratic in the relativistic gravitational potential $u=G(m_1 +m_2)/(c^2 r)$) significantly increase the effective tidal polarizability of neutron stars by a distance-dependent amplification factor of the form $1 + α_1 \, u + α_2 \, u^2 +...$ where, say for an equal-mass binary, $α_1=5/4=1.25$ (as previously known) and $α_2=85/14\simeq6.07143$ (as determined here for the first time). We argue that higher-order relativistic effects will lead to further amplification, and we suggest a Padé-type way of resumming them. We recommend to test our results by comparing resolution-extrapolated numerical simulations of inspiralling-binary neutron stars to their effective one body description.

gr-qc↗
arXiv2012

Measurability of the tidal polarizability of neutron stars in late-inspiral gravitational-wave signals

The gravitational wave signal from a binary neutron star inspiral contains information on the nuclear equation of state. This information is contained in a combination of the tidal polarizability parameters of the two neutron stars and is clearest in the late inspiral, just before merger. We use the recently defined tidal extension of the effective one-body formalism to construct a controlled analytical description of the frequency-domain phasing of neutron star inspirals up to merger. Exploiting this analytical description we find that the tidal polarizability parameters of neutron stars can be measured by the advanced LIGO-Virgo detector network from gravitational wave signals having a reasonable signal-to-noise ratio of $ρ=16$. This measurability result seems to hold for all the nuclear equations of state leading to a maximum mass larger than $1.97M_\odot$. We also propose a promising new way of extracting information on the nuclear equation of state from a coherent analysis of an ensemble of gravitational wave observations of separate binary merger events.

gr-qc↗
arXiv2012

Theoretical Aspects of the Equivalence Principle

We review several theoretical aspects of the Equivalence Principle (EP). We emphasize the unsatisfactory fact that the EP maintains the absolute character of the coupling constants of physics while General Relativity, and its generalizations (Kaluza-Klein,..., String Theory), suggest that all absolute structures should be replaced by dynamical entities. We discuss the EP-violation phenomenology of dilaton-like models, which is likely to be dominated by the linear superposition of two effects: a signal proportional to the nuclear Coulomb energy, related to the variation of the fine-structure constant, and a signal proportional to the surface nuclear binding energy, related to the variation of the light quark masses. We recall the various theoretical arguments (including a recently proposed anthropic argument) suggesting that the EP be violated at a small, but not unmeasurably small level. This motivates the need for improved tests of the EP. These tests are probing new territories in physics that are related to deep, and mysterious, issues in fundamental physics.

gr-qc↗
arXiv2011

Energy versus Angular Momentum in Black Hole Binaries

Using accurate numerical relativity simulations of (nonspinning) black-hole binaries with mass ratios 1:1, 2:1 and 3:1 we compute the gauge invariant relation between the (reduced) binding energy $E$ and the (reduced) angular momentum $j$ of the system. We show that the relation $E(j)$ is an accurate diagnostic of the dynamics of a black-hole binary in a highly relativistic regime. By comparing the numerical-relativity $E^{\rm NR} (j)$ curve with the predictions of several analytic approximation schemes, we find that, while the usual, non-resummed post-Newtonian-expanded $E^{\rm PN} (j)$ relation exhibits large and growing deviations from $E^{\rm NR} (j)$, the prediction of the effective one-body formalism, based purely on known analytical results (without any calibration to numerical relativity), agrees strikingly well with the numerical-relativity results.

gr-qc↗
arXiv2011

Accurate numerical simulations of inspiralling binary neutron stars and their comparison with effective-one-body analytical models

Binary neutron-star systems represent one of the most promising sources of gravitational waves. In order to be able to extract important information, notably about the equation of state of matter at nuclear density, it is necessary to have in hands an accurate analytical model of the expected waveforms. Following our recent work, we here analyze more in detail two general-relativistic simulations spanning about 20 gravitational-wave cycles of the inspiral of equal-mass binary neutron stars with different compactnesses, and compare them with a tidal extension of the effective-one-body (EOB) analytical model. The latter tidally extended EOB model is analytically complete up to the 1.5 post-Newtonian level, and contains an analytically undetermined parameter representing a higher-order amplification of tidal effects. We find that, by calibrating this single parameter, the EOB model can reproduce, within the numerical error, the two numerical waveforms essentially up to the merger. By contrast, analytical models (either EOB, or Taylor-T4) that do not incorporate such a higher-order amplification of tidal effects, build a dephasing with respect to the numerical waveforms of several radians.

gr-qc↗
arXiv2011

Spatial variation of fundamental couplings and Lunar Laser Ranging

If the fundamental constants of nature have a cosmic spatial variation, there will in general be extra forces with a preferred direction in space which violate the equivalence principle. We show that the millimeter-precision Apache Point Observatory Lunar Laser-ranging Operation provides a very sensitive probe of such variation that has the capability of detecting a cosmic gradient of the ratio between the quark masses and the strong interaction scale at the level with the gradient of ln (m_quark/Lambda_QCD) ~ 2.6 x 10^-6 Glyr^-1, which is comparable to the cosmic gradients suggested by the recently reported measurements of Webb et al. We also point out the capability of presently planned improved equivalence principle tests, at the Delta g/g < 10^-17 level, to probe similar cosmic gradients.

gr-qc↗
arXiv2011

Quantum Einstein-Dirac Bianchi Universes

We study the mini--superspace quantization of spatially homogeneous (Bianchi) cosmological universes sourced by a Dirac spinor field. The quantization of the homogeneous spinor leads to a finite-dimensional fermionic Hilbert space and thereby to a multi-component Wheeler-DeWitt equation whose main features are: (i) the presence of spin-dependent Morse-type potentials, and (ii) the appearance of a q-number squared-mass term, which is of order ${\cal O}(\hbar^2)$, and which is affected by ordering ambiguities. We give the exact quantum solution of the Bianchi type-II system (which contains both scattering states and bound states), and discuss the main qualitative features of the quantum dynamics of the (classically chaotic) Bianchi type-IX system. We compare the exact quantum dynamics of fermionic cosmological billiards to previous works that described the spinor field as being either classical or Grassmann-valued.

gr-qc↗
arXiv2011

Statistical Properties of Cosmological Billiards

Belinski, Khalatnikov and Lifshitz (BKL) pioneered the study of the statistical properties of the never-ending oscillatory behavior (among successive Kasner epochs) of the geometry near a space-like singularity. We show how the use of a "cosmological billiard" description allows one to refine and deepen the understanding of these statistical properties. Contrary to previous treatments, we do not quotient the dynamics by its discrete symmetry group (of order 6), thereby uncovering new phenomena, such as correlations between the successive billiard corners in which the oscillations take place. Starting from the general integral invariants of Hamiltonian systems, we show how to construct invariant measures for various projections of the cosmological-billiard dynamics. In particular, we exhibit, for the first time, a (non-normalizable) invariant measure on the "Kasner circle" which parametrizes the exponents of successive Kasner epochs. Finally, we discuss the relation between: (i) the unquotiented dynamics of the Bianchi IX (a, b, c or mixmaster) model; (ii) its quotienting by the group of permutations of (a, b, c); and (iii) the billiard dynamics that arose in recent studies suggesting the hidden presence of Kac-Moody symmetries in cosmological billiards.

gr-qc↗
arXiv2010

Analytic modelling of tidal effects in the relativistic inspiral of binary neutron stars

To detect the gravitational-wave (GW) signal from binary neutron stars and extract information about the equation of state of matter at nuclear density, it is necessary to match the signal with a bank of accurate templates. We present the two longest (to date) general-relativistic simulations of equal-mass binary neutron stars with different compactnesses, C=0.12 and C=0.14, and compare them with a tidal extension of the effective-one-body (EOB)model. The typical numerical phasing errors over the $\simeq 22$ GW cycles are $Δϕ\simeq \pm 0.24$ rad. By calibrating only one parameter (representing a higher-order amplification of tidal effects), the EOB model can reproduce, within the numerical error, the two numerical waveforms essentially up to the merger. By contrast, the third post-Newtonian Taylor-T4 approximant with leading-order tidal corrections dephases with respect to the numerical waveforms by several radians.

gr-qc↗
arXiv2010

Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism

Using a recently presented numerical code for calculating the Lorenz-gauge gravitational self-force (GSF), we compute the $O(m)$ conservative correction to the precession rate of the small-eccentricity orbits of a particle of mass $m$ moving around a Schwarzschild black hole of mass ${\mathsf M}\gg m$. Specifically, we study the gauge-invariant function $ρ(x)$, where $ρ$ is defined as the $O(m)$ part of the dimensionless ratio $(\hatΩ_r/\hatΩ_φ)^2$ between the squares of the radial and azimuthal frequencies of the orbit, and where $x=[Gc^{-3}({\mathsf M}+m)\hatΩ_φ]^{2/3}$ is a gauge-invariant measure of the dimensionless gravitational potential (mass over radius) associated with the mean circular orbit. Our GSF computation of the function $ρ(x)$ in the interval $0<x\leq 1/6$ determines, for the first time, the {\em strong-field behavior} of a combination of two of the basic functions entering the Effective One Body (EOB) description of the conservative dynamics of binary systems. We show that our results agree well in the weak-field regime (small $x$) with the 3rd post-Newtonian (PN) expansion of the EOB results, and that this agreement is improved when taking into account the analytic values of some of the logarithmic-running terms occurring at higher PN orders. Furthermore, we demonstrate that GSF data give access to higher-order PN terms of $ρ(x)$ and can be used to set useful new constraints on the values of yet-undetermined EOB parameters. Most significantly, we observe that an {\em excellent global representation} of $ρ(x)$ can be obtained using a simple `two-point' Padé approximant which combines 3PN knowledge at $x=0$ with GSF information at a single strong-field point (say, $x=1/6$).

gr-qc↗
arXiv2010

Phenomenology of the Equivalence Principle with Light Scalars

Light scalar particles with couplings of sub-gravitational strength, which can generically be called 'dilatons', can produce violations of the equivalence principle. However, in order to understand experimental sensitivities one must know the coupling of these scalars to atomic systems. We report here on a study of the required couplings. We give a general Lagrangian with five independent dilaton parameters and calculate the "dilaton charge" of atomic systems for each of these. Two combinations are particularly important. One is due to the variations in the nuclear binding energy, with a sensitivity scaling with the atomic number as $A^{-1/3}$. The other is due to electromagnetism. We compare limits on the dilaton parameters from existing experiments.

gr-qc↗
arXiv2010

Equivalence Principle Violations and Couplings of a Light Dilaton

We consider possible violations of the equivalence principle through the exchange of a light `dilaton-like' scalar field. Using recent work on the quark-mass dependence of nuclear binding, we find that the dilaton-quark-mass coupling induces significant equivalence-principle-violating effects varying like the inverse cubic root of the atomic number - A^{-1/3}. We provide a general parameterization of the scalar couplings, but argue that two parameters are likely to dominate the equivalence-principle phenomenology. We indicate the implications of this framework for comparing the sensitivities of current and planned experimental tests of the equivalence principle.

gr-qc↗
arXiv2009

Sugawara-type constraints in hyperbolic coset models

In the conjectured correspondence between supergravity and geodesic models on infinite-dimensional hyperbolic coset spaces, and E10/K(E10) in particular, the constraints play a central role. We present a Sugawara-type construction in terms of the E10 Noether charges that extends these constraints infinitely into the hyperbolic algebra, in contrast to the truncated expressions obtained in arXiv:0709.2691 that involved only finitely many generators. Our extended constraints are associated to an infinite set of roots which are all imaginary, and in fact fill the closed past light-cone of the Lorentzian root lattice. The construction makes crucial use of the E10 Weyl group and of the fact that the E10 model contains both D=11 supergravity and D=10 IIB supergravity. Our extended constraints appear to unite in a remarkable manner the different canonical constraints of these two theories. This construction may also shed new light on the issue of `open constraint algebras' in traditional canonical approaches to gravity.

hep-th↗
arXiv2009

Relativistic tidal properties of neutron stars

We study the various linear responses of neutron stars to external relativistic tidal fields. We focus on three different tidal responses, associated to three different tidal coefficients: (i) a gravito-electric-type coefficient Gμ_\ell=[length]^{2\ell+1} measuring the \ell^{th}-order mass multipolar moment GM_{a_1... a_\ell} induced in a star by an external \ell^{th}-order gravito-electric tidal field G_{a_1... a_\ell}; (ii) a gravito-magnetic-type coefficient Gσ_\ell=[length]^{2\ell+1} measuring the \ell^{th} spin multipole moment G S_{a_1... a_\ell} induced in a star by an external \ell^{th}-order gravito-magnetic tidal field H_{a_1... a_\ell}; and (iii) a dimensionless ``shape'' Love number h_\ell measuring the distortion of the shape of the surface of a star by an external \ell^{th}-order gravito-electric tidal field. All the dimensionless tidal coefficients Gμ_\ell/R^{2\ell+1}, Gσ_ł/R^{2\ell+1} and h_\ell (where R is the radius of the star) are found to have a strong sensitivity to the value of the star's ``compactness'' c\equiv GM/(c_0^2 R) (where we indicate by c_0 the speed of light). In particular, Gμ_ł/R^{2ł+1}\sim k_\ell is found to strongly decrease, as c increases, down to a zero value as c is formally extended to the ``black-hole (BH) limit'' c^{BH}=1/2. The shape Love number h_\ell is also found to significantly decrease as c increases, though it does not vanish in the formal limit c\to c^{BH}. The formal vanishing of μ_\ell and σ_\ell as c\to c^{BH} is a consequence of the no-hair properties of black holes; this suggests, but in no way proves, that the effective action describing the gravitational interactions of black holes may not need to be augmented by nonminimal worldline couplings.

gr-qc↗
arXiv2009

Fermionic Kac-Moody Billiards and Supergravity

We study the "fermionic billiards", i.e. the chaotic dynamics of the gravitino, that arise in the near-spacelike-singularity limit of eleven-dimensional supergravity and of its dimensional truncations (notably four-dimensional simple supergravity). By exploiting the gravity-coset correspondence, we show that the billiard dynamics of the gravitino is described by a `spin extension' of the E(10) Weyl group, namely as a product of 90 degree `vector-spinor rotations' along certain simple-root-related generators of the maximal compact subalgebra K(E(10)) of the hyperbolic Kac--Moody algebra E(10). The `super-billiard' that combines the bosonic and fermionic billiards is found to have a remarkably simple structure, which exhibits a striking analogy with a polarized photon propagating in the ten-dimensional Lorentzian Weyl chamber of E(10).

hep-th↗