Gravitational waves and dynamics of compact binary systems

Part A of this article is devoted to the general investigation of the gravitational-wave emission by post-Newtonian sources. We show how the radiation field far from the source, as well as its near-zone inner gravitational field, can (in principle) be calculated in terms of the matter stress-energy tensor up to any order in the post-Newtonian expansion. Part B presents some recent applications to the problems of the dynamics and gravitational-wave flux of compact binary systems. The precision reached in these developments corresponds to the third post-Newtonian approximation.Comment: Plenary lecture given at the 16th International Conference on General Relativity and Gravitation. To appear in the proceedings, edited by N.T. Bishop and S.D. Maharaj, World Scientifi

On the accuracy of the post-Newtonian approximation

We apply standard post-Newtonian methods in general relativity to locate the innermost circular orbit (ICO) of irrotational and corotational binary black-hole systems. We find that the post-Newtonian series converges well when the two masses are comparable. We argue that the result for the ICO which is predicted by the third post-Newtonian (3PN) approximation is likely to be very close to the ``exact'' solution, within 1% of fractional accuracy or better. The 3PN result is also in remarkable agreement with a numerical calculation of the ICO in the case of two corotating black holes moving on exactly circular orbits. The behaviour of the post-Newtonian series suggests that the gravitational dynamics of two bodies of comparable masses does not resemble that of a test particle on a Schwarzschild background. This leads us to question the validity of some post-Newtonian resummation techniques that are based on the idea that the field generated by two black holes is a deformation of the Schwarzschild space-time.Comment: 20 pages, in "2001: a relativistic spacetime odyssey", Proc. of the 25th Johns Hopkins Workshop, I. Ciufolini, D. Dominici and L. Lusanna (eds.), World Scientific, p. 411 (2001

Dipolar Particles in General Relativity

The dynamics of "dipolar particles", i.e. particles endowed with a four-vector mass dipole moment, is investigated using an action principle in general relativity. The action is a specific functional of the particle's world line, and of the dipole moment vector, considered as a dynamical variable. The first part of the action is inspired by that of a particle with spin moving on an arbitrary gravitational background. The second part is intended to describe, at some effective level, the internal non-gravitational force linking together the "microscopic" constituents of the dipole. We find that some solutions of the equations of motion and evolution of the dipolar particles correspond to an equilibrium state for the dipole moment in a gravitational field. Under some hypothesis we show that a fluid of dipolar particles, supposed to constitute the dark matter, reproduces the modified Newtonian dynamics (MOND) in the non relativistic limit. We recover the main characteristics of a recently proposed quasi-Newtonian model of "gravitational polarization".Comment: 33 pages, 6 figures, to appear in Classical and Quantum Gravit

Gravitational Radiation from Two-Body Systems

Thanks to the new generation of gravitational wave detectors LIGO and VIRGO, the theory of general relativity will face new and important confrontations to observational data with unprecedented precision. Indeed the detection and analysis of the gravitational waves from compact binary star systems requires beforehand a very precise solution of the two-body problem within general relativity. The approximation currently used to solve this problem is the post-Newtonian one, and must be pushed to high order in order to describe with sufficient accuracy (given the sensitivity of the detectors) the inspiral phase of compact bodies, which immediately precedes their final merger. The resulting post-Newtonian ``templates'' are currently known to 3.5PN order, and are used for searching and deciphering the gravitational wave signals in VIRGO and LIGO.Comment: 19 pages, to appear in the Proceedings of the Spanish Relativity Meeting ``A Century of Relativity Physics'' (ERE05), Edited by Lysiane Mornas and Joaquin Diaz-Alons

General Relativistic Dynamics of Compact Binary Systems

The equations of motion of compact binary systems have been derived in the post-Newtonian (PN) approximation of general relativity. The current level of accuracy is 3.5PN order. The conservative part of the equations of motion (neglecting the radiation reaction damping terms) is deducible from a generalized Lagrangian in harmonic coordinates, or equivalently from an ordinary Hamiltonian in ADM coordinates. As an application we investigate the problem of the dynamical stability of circular binary orbits against gravitational perturbations up to the 3PN order. We find that there is no innermost stable circular orbit or ISCO at the 3PN order for equal masses.Comment: 13 pages, to appear in the special issue of the Comptes rendus de l'Academie des Sciences de Paris on "Observations of black holes and extreme gravitational events", edited by Daniel Roua

Post-Newtonian Expansion of Gravitational Radiation

The post-Newtonian expansion appears to be a relevant tool for predicting the gravitational waveforms generated by some astrophysical systems such as binaries. In particular, inspiralling compact binaries are well-modelled by a system of two point-particles moving on a quasi-circular orbit whose decay by emission of gravitational radiation is described by a post-Newtonian expansion. In this paper we summarize the basics of the computation by means of a series of multipole moments of the exterior field generated by an isolated source in the post-Newtonian approximation. This computation relies on an ansatz of matching the exterior multipolar field to the inner field of a slowly-moving source. The formalism can be applied to point-particles at the price of a further ansatz, that the infinite self-field of point-particles can be regularized in a certain way. As it turns out, the concept of point-particle requires a precise definition in high post-Newtonian approximations of general relativity.Comment: In Black Holes and Gravitational Waves, Proceedings of the 9th Yukawa International Seminar, T. Nakamura and H. Kodama (eds.), Prog. Theor. Phys. Suppl. No. 136, 146 (1999