Gravitational-Wave Inspiral of Compact Binary Systems to 7/2 Post-Newtonian Order

The inspiral of compact binaries, driven by gravitational-radiation reaction, is investigated through 7/2 post-Newtonian (3.5PN) order beyond the quadrupole radiation. We outline the derivation of the 3.5PN-accurate binary's center-of-mass energy and emitted gravitational flux. The analysis consistently includes the relativistic effects in the binary's equations of motion and multipole moments, as well as the contributions of tails, and tails of tails, in the wave zone. However the result is not fully determined because of some physical incompleteness, present at the 3PN order, of the model of point-particle and the associated Hadamard-type self-field regularization. The orbital phase, whose prior knowledge is crucial for searching and analyzing the inspiral signal, is computed from the standard energy balance argument.Comment: 12 pages, version which includes the correction of an Erratum to be published in Phys. Rev. D (2005

Efficient Monte Carlo for high excursions of Gaussian random fields

Our focus is on the design and analysis of efficient Monte Carlo methods for computing tail probabilities for the suprema of Gaussian random fields, along with conditional expectations of functionals of the fields given the existence of excursions above high levels, b. Na\"{i}ve Monte Carlo takes an exponential, in b, computational cost to estimate these probabilities and conditional expectations for a prescribed relative accuracy. In contrast, our Monte Carlo procedures achieve, at worst, polynomial complexity in b, assuming only that the mean and covariance functions are H\"{o}lder continuous. We also explain how to fine tune the construction of our procedures in the presence of additional regularity, such as homogeneity and smoothness, in order to further improve the efficiency.Comment: Published in at http://dx.doi.org/10.1214/11-AAP792 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Gravitational wave forms for a three-body system in Lagrange's orbit: parameter determinations and a binary source test

Continuing work initiated in an earlier publication [Torigoe et al. Phys. Rev. Lett. {\bf 102}, 251101 (2009)], gravitational wave forms for a three-body system in Lagrange's orbit are considered especially in an analytic method. First, we derive an expression of the three-body wave forms at the mass quadrupole, octupole and current quadrupole orders. By using the expressions, we solve a gravitational-wave {\it inverse} problem of determining the source parameters to this particular configuration (three masses, a distance of the source to an observer, and the orbital inclination angle to the line of sight) through observations of the gravitational wave forms alone. For this purpose, the chirp mass to a three-body system in the particular configuration is expressed in terms of only the mass ratios by deleting initial angle positions. We discuss also whether and how a binary source can be distinguished from a three-body system in Lagrange's orbit or others.Comment: 21 pages, 3 figures, 1 table; text improved, typos corrected; accepted for publication in PR

Gravitational waves from inspiralling compact binaries: Energy loss and waveform to second--post-Newtonian order

Gravitational waves generated by inspiralling compact binaries are investigated to the second--post-Newtonian (2PN) approximation of general relativity. Using a recently developed 2PN-accurate wave generation formalism, we compute the gravitational waveform and associated energy loss rate from a binary system of point-masses moving on a quasi-circular orbit. The crucial new input is our computation of the 2PN-accurate ``source'' quadrupole moment of the binary. Tails in both the waveform and energy loss rate at infinity are explicitly computed. Gravitational radiation reaction effects on the orbital frequency and phase of the binary are deduced from the energy loss. In the limiting case of a very small mass ratio between the two bodies we recover the results obtained by black hole perturbation methods. We find that finite mass ratio effects are very significant as they increase the 2PN contribution to the phase by up to 52\%. The results of this paper should be of use when deciphering the signals observed by the future LIGO/VIRGO network of gravitational-wave detectors.Comment: 43 pages, LaTeX-ReVTeX, no figures

The Statistical Mechanics of Horizons and Black Hole Thermodynamics

Although we know that black holes are characterized by a temperature and an entropy, we do not yet have a satisfactory microscopic ``statistical mechanical'' explanation for black hole thermodynamics. I describe a new approach that attributes the thermodynamic properties to ``would-be gauge'' degrees of freedom that become dynamical on the horizon. For the (2+1)-dimensional black hole, this approach gives the correct entropy. (Talk given at the Pacific Conference on Gravitation and Cosmology, Seoul, February 1996.)Comment: 11 pages, LaTe

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-CDM) at cosmological scales, and the phenomenology of the modified Newtonian dynamics (MOND) 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.Comment: 11 pages, 2 figures; minor stylistic corrections, added references, added appendix; to appear in Phys. Rev.

Post-Newtonian approximation for isolated systems calculated by matched asymptotic expansions

Two long-standing problems with the post-Newtonian approximation for isolated slowly-moving systems in general relativity are: (i) the appearance at high post-Newtonian orders of divergent Poisson integrals, casting a doubt on the soundness of the post-Newtonian series; (ii) the domain of validity of the approximation which is limited to the near-zone of the source, and prevents one, a priori, from incorporating the condition of no-incoming radiation, to be imposed at past null infinity. In this article, we resolve the problem (i) by iterating the post-Newtonian hierarchy of equations by means of a new (Poisson-type) integral operator that is free of divergencies, and the problem (ii) by matching the post-Newtonian near-zone field to the exterior field of the source, known from previous work as a multipolar-post-Minkowskian expansion satisfying the relevant boundary conditions at infinity. As a result, we obtain an algorithm for iterating the post-Newtonian series up to any order, and we determine the terms, present in the post-Newtonian field, that are associated with the gravitational-radiation reaction onto an isolated slowly-moving matter system.Comment: 61 pages, to appear in Phys. Rev.

Lorentzian regularization and the problem of point-like particles in general relativity

The two purposes of the paper are (1) to present a regularization of the self-field of point-like particles, based on Hadamard's concept of ``partie finie'', that permits in principle to maintain the Lorentz covariance of a relativistic field theory, (2) to use this regularization for defining a model of stress-energy tensor that describes point-particles in post-Newtonian expansions (e.g. 3PN) of general relativity. We consider specifically the case of a system of two point-particles. We first perform a Lorentz transformation of the system's variables which carries one of the particles to its rest frame, next implement the Hadamard regularization within that frame, and finally come back to the original variables with the help of the inverse Lorentz transformation. The Lorentzian regularization is defined in this way up to any order in the relativistic parameter 1/c^2. Following a previous work of ours, we then construct the delta-pseudo-functions associated with this regularization. Using an action principle, we derive the stress-energy tensor, made of delta-pseudo-functions, of point-like particles. The equations of motion take the same form as the geodesic equations of test particles on a fixed background, but the role of the background is now played by the regularized metric.Comment: 34 pages, to appear in J. Math. Phy