Alexandre Le Tiec

Dipolar Dark Matter and Dark Energy

In previous work [L. Blanchet and A. Le Tiec, Phys. Rev. D 78, 024031 (2008)], a model of dark matter and dark energy based on the concept of gravitational polarization was investigated. This model was shown to recover the concordance cosmological scenario ({lambda}-cold dark matter) at cosmological scales, and the phenomenology of the modified Newtonian dynamics at galactic scales. In this article we prove that the model can be formulated with a simple and physically meaningful matter action in general relativity. We also provide alternative derivations of the main results of the model, and some details on the variation of the action.

Model of Dark Matter and Dark Energy Based on Gravitational Polarization

A model of dark matter and dark energy based on the concept of gravitational polarization is investigated. We propose an action in standard general relativity for describing, at some effective or phenomenological level, the dynamics of a dipolar medium, i.e. one endowed with a dipole moment vector, and polarizable in a gravitational field. Using first-order cosmological perturbations, we show that the dipolar fluid is undistinguishable from standard dark energy (a cosmological constant �) plus standard dark matter (a pressureless perfect fluid), and therefore benefits from the successes of the �-CDM (�-cold dark matter) scenario at cosmological scales. Invoking an argument of “weak clusterisation” of the mass distribution of dipole moments, we find that the dipolar dark matter reproduces the phenomenology of the modified Newtonian dynamics (MOND) at galactic scales. The dipolar medium action naturally contains a cosmological constant, and we show that if the

The First Law of Binary Black Hole Mechanics in General Relativity and Post-Newtonian Theory

First laws of black hole mechanics, or thermodynamics, come in a variety of different forms. In this paper, from a purely post-Newtonian (PN) analysis, we obtain a first law for binary systems of point masses moving along an exactly circular orbit. Our calculation is valid through 3PN order and includes, in addition, the contributions of logarithmic terms at 4PN and 5PN orders. This first law of binary point-particle mechanics is then derived from first principles in general relativity, and analogies are drawn with the single and binary black hole cases. Some consequences of the first law are explored for PN spacetimes. As one such consequence, a simple relation between the PN binding energy of the binary system and Detweilers redshift observable is established. Through it, we are able to determine with high precision the numerical values of some previously unknown high order PN coefficients in the circular-orbit binding energy. Finally, we propose new gauge invariant notions for the energy and angular momentum of a particle in a binary system.

The complete non-spinning effective-one-body metric at linear order in the mass ratio

Although the ‘‘two-body problem’’ cannot be solved analytically in the general theory of relativity, at least two approximation methods can be used to tackle it. The first one dates back to Einstein’s 1915 calculation of the relativistic perihelion advance of Mercury’s orbit [1], and is based on a perturbative treatment in powers of the ratio v=c between the binary’s relative velocity v (in the centerof-mass frame) and the vacuum speed of light c. At the lowest order of approximation, this approach gives back the well-known Newtonian solution, and is therefore dubbed ‘‘post-Newtonian’’ (PN) expansion; see e.g.

High-Order Post-Newtonian Fit of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry

We continue a previous work on the comparison between the post-Newtonian (PN) approximation and the gravitational self-force (SF) analysis of circular orbits in a Schwarzschild background. We show that the numerical SF data contain physical information corresponding to extremely high PN approximations. We nd that knowing analytically determined appropriate PN parameters helps tremendously in allowing the numerical data to be used to obtain higher order PN coecients. Using standard PN theory we compute analytically the leading 4PN and the next-to-leading 5PN logarithmic terms in the conservative part of the dynamics of a compact binary system. The numerical perturbative SF results support well the analytic PN calculations through rst order in the mass ratio, and are used to accurately measure the 4PN and 5PN non-logarithmic coecients in a particular gauge invariant observable. Furthermore we are able to give estimates of higher order contributions up to the 7PN level. We also conrm with high precision the value of the 3PN

Gravitational Self-Force Correction to the Binding Energy of Compact Binary Systems

Using the first law of binary black-hole mechanics, we compute the binding energy E and total angular momentum J of two nonspinning compact objects moving on circular orbits with frequency Ω, at leading order beyond the test-particle approximation. By minimizing E(Ω) we recover the exact frequency shift of the Schwarzschild innermost stable circular orbit induced by the conservative piece of the gravitational self-force. Comparing our results for the coordinate-invariant relation E(J) to those recently obtained from numerical simulations of comparable-mass nonspinning black-hole binaries, we find a remarkably good agreement, even in the strong-field regime. Our findings confirm that the domain of validity of perturbative calculations may extend well beyond the extreme mass-ratio limit.

Periastron advance in black-hole binaries.

The general relativistic (Mercury-type) periastron advance is calculated here for the first time with exquisite precision in full general relativity. We use accurate numerical relativity simulations of spinless black-hole binaries with mass ratios 1/8≤m(1)/m(2)≤1 and compare with the predictions of several analytic approximation schemes. We find the effective-one-body model to be remarkably accurate and, surprisingly, so also the predictions of self-force theory [replacing m(1)/m(2)→m(1)m(2)/(m(1)+m(2))(2)]. Our results can inform a universal analytic model of the two-body dynamics, crucial for ongoing and future gravitational-wave searches.

Gravitational Self-Torque and Spin Precession in Compact Binaries

We calculate the effect of self-interaction on the “geodetic” spin precession of a compact body in a strong-field orbit around a black hole. Specifically, we consider the spin precession angle ? per radian of orbital revolution for a particle carrying mass ? and spin s?(G/c)?2 in a circular orbit around a Schwarzschild black hole of mass M??. We compute ? through O(?/M) in perturbation theory, i.e, including the correction ?? (obtained numerically) due to the torque exerted by the conservative piece of the gravitational self-field. Comparison with a post-Newtonian (PN) expression for ??, derived here through 3PN order, shows good agreement but also reveals strong-field features which are not captured by the latter approximation. Our results can inform semianalytical models of the strong-field dynamics in astrophysical binaries, important for ongoing and future gravitational-wave searches

Gravitational Self-Force Correction to the Innermost Stable Circular Equatorial Orbit of a Kerr Black Hole

For a self-gravitating particle of mass μ in orbit around a Kerr black hole of mass M ≫ μ, we compute the O(μ/M) shift in the frequency of the innermost stable circular equatorial orbit due to the conservative piece of the gravitational self-force acting on the particle. Our treatment is based on a Hamiltonian formulation of the dynamics in terms of geodesic motion in a certain locally defined effective smooth spacetime. We recover the same result using the so-called first law of binary black-hole mechanics. We give numerical results for the innermost stable circular equatorial orbit frequency shift as a function of the black holes spin amplitude, and compare with predictions based on the post-Newtonian approximation and the effective one-body model. Our results provide an accurate strong-field benchmark for spin effects in the general-relativistic two-body problem.

First Law of Mechanics for Black Hole Binaries with Spins

We use the canonical Hamiltonian formalism to generalize to spinning point particles the first law of mechanics established for binary systems of nonspinning point masses moving on circular orbits [A. Le Tiec, L. Blanchet, and B.F. Whiting, Phys. Rev. D 85, 064039 (2012)]. We find that the redshift observable of each particle is related in a very simple manner to the canonical Hamiltonian and, more generally, to a class of Fokker-type Hamiltonians. Our results are valid through linear order in the spin of each particle, but hold also for quadratic couplings between the spins of different particles. The knowledge of spin effects in the Hamiltonian allows us to compute spin-orbit terms in the redshift variable through 2.5PN order, for circular orbits and spins aligned or anti-aligned with the orbital angular momentum. To describe extended bodies such as black holes, we supplement the first law for spinning point-particle binaries with some ‘‘constitutive relations’’ that can be used for diagnosis of spin measurements in quasiequilibrium initial data.