2,184 research outputs found
Gravitational radiation reaction in the equations of motion of compact binaries to 3.5 post-Newtonian order
We compute the radiation reaction force on the orbital motion of compact
binaries to the 3.5 post-Newtonian (3.5PN) approximation, i.e. one PN order
beyond the dominant effect. The method is based on a direct PN iteration of the
near-zone metric and equations of motion of an extended isolated system, using
appropriate ``asymptotically matched'' flat-space-time retarded potentials. The
formalism is subsequently applied to binary systems of point particles, with
the help of the Hadamard self-field regularisation. Our result is the 3.5PN
acceleration term in a general harmonic coordinate frame. Restricting the
expression to the centre-of-mass frame, we find perfect agreement with the
result derived in a class of coordinate systems by Iyer and Will using the
energy and angular momentum balance equations.Comment: 28 pages, references added, to appear in Classical and Quantum
Gravit
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.
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
Hadamard Regularization
Motivated by the problem of the dynamics of point-particles in high
post-Newtonian (e.g. 3PN) approximations of general relativity, we consider a
certain class of functions which are smooth except at some isolated points
around which they admit a power-like singular expansion. We review the concepts
of (i) Hadamard ``partie finie'' of such functions at the location of singular
points, (ii) the partie finie of their divergent integral. We present and
investigate different expressions, useful in applications, for the latter
partie finie. To each singular function, we associate a partie-finie (Pf)
pseudo-function. The multiplication of pseudo-functions is defined by the
ordinary (pointwise) product. We construct a delta-pseudo-function on the class
of singular functions, which reduces to the usual notion of Dirac distribution
when applied on smooth functions with compact support. We introduce and analyse
a new derivative operator acting on pseudo-functions, and generalizing, in this
context, the Schwartz distributional derivative. This operator is uniquely
defined up to an arbitrary numerical constant. Time derivatives and partial
derivatives with respect to the singular points are also investigated. In the
course of the paper, all the formulas needed in the application to the physical
problem are derived.Comment: 50 pages, to appear in Journal of Mathematical Physic
Time-symmetric initial data for binary black holes in numerical relativity
We look for physically realistic initial data in numerical relativity which
are in agreement with post-Newtonian approximations. We propose a particular
solution of the time-symmetric constraint equation, appropriate to two
momentarily static black holes, in the form of a conformal decomposition of the
spatial metric. This solution is isometric to the post-Newtonian metric up to
the 2PN order. It represents a non-linear deformation of the solution of Brill
and Lindquist, i.e. an asymptotically flat region is connected to two
asymptotically flat (in a certain weak sense) sheets, that are the images of
the two singularities through appropriate inversion transformations. The total
ADM mass M as well as the individual masses m_1 and m_2 (when they exist) are
computed by surface integrals performed at infinity. Using second order
perturbation theory on the Brill-Lindquist background, we prove that the
binary's interacting mass-energy M-m_1-m_2 is well-defined at the 2PN order and
in agreement with the known post-Newtonian result.Comment: 27 pages, to appear in Phys. Rev.
Detection of the ultranarrow temporal correlation of twin beams via sum-frequency generation
We demonstrate the ultranarrow temporal correlation (6 fs full width half
maximum) of twin beams generated by parametric down-conversion, by using the
inverse process of sum-frequency generation. The result relies on an achromatic
imaging of a huge bandwith of twin beams and on a careful control of their
spatial degrees of freedom. The detrimental effects of spatial filtering and of
imperfect imaging are shown toghether with the theoretical model used to
describe the results
Gravitational field and equations of motion of spinning compact binaries to 2.5 post-Newtonian order
We derive spin-orbit coupling effects on the gravitational field and
equations of motion of compact binaries in the 2.5 post-Newtonian approximation
to general relativity, one PN order beyond where spin effects first appear. Our
method is based on that of Blanchet, Faye, and Ponsot, who use a post-Newtonian
metric valid for general (continuous) fluids and represent pointlike compact
objects with a delta-function stress-energy tensor, regularizing divergent
terms by taking the Hadamard finite part. To obtain post-Newtonian spin
effects, we use a different delta-function stress-energy tensor introduced by
Bailey and Israel. In a future paper we will use the 2.5PN equations of motion
for spinning bodies to derive the gravitational-wave luminosity and phase
evolution of binary inspirals, which will be useful in constructing matched
filters for signal analysis. The gravitational field derived here may help in
posing initial data for numerical evolutions of binary black hole mergers.Comment: 18 pages, no figur
Finite mass self-similar blowing-up solutions of a chemotaxis system with non-linear diffusion
For a specific choice of the diffusion, the parabolic-elliptic
Patlak-Keller-Segel system with non-linear diffusion (also referred to as the
quasi-linear Smoluchowski-Poisson equation) exhibits an interesting threshold
phenomenon: there is a critical mass such that all the solutions with
initial data of mass smaller or equal to exist globally while the
solution blows up in finite time for a large class of initial data with mass
greater than . Unlike in space dimension 2, finite mass self-similar
blowing-up solutions are shown to exist in space dimension
Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries
The article reviews the current status of a theoretical approach to the
problem of the emission of gravitational waves by isolated systems in the
context of general relativity. Part A of the article deals with general
post-Newtonian sources. The exterior field of the source is investigated by
means of a combination of analytic post-Minkowskian and multipolar
approximations. The physical observables in the far-zone of the source are
described by a specific set of radiative multipole moments. By matching the
exterior solution to the metric of the post-Newtonian source in the near-zone
we obtain the explicit expressions of the source multipole moments. The
relationships between the radiative and source moments involve many non-linear
multipole interactions, among them those associated with the tails (and
tails-of-tails) of gravitational waves. Part B of the article is devoted to the
application to compact binary systems. We present the equations of binary
motion, and the associated Lagrangian and Hamiltonian, at the third
post-Newtonian (3PN) order beyond the Newtonian acceleration. The
gravitational-wave energy flux, taking consistently into account the
relativistic corrections in the binary moments as well as the various tail
effects, is derived through 3.5PN order with respect to the quadrupole
formalism. The binary's orbital phase, whose prior knowledge is crucial for
searching and analyzing the signals from inspiralling compact binaries, is
deduced from an energy balance argument.Comment: 109 pages, 1 figure; this version is an update of the Living Review
article originally published in 2002; available on-line at
http://www.livingreviews.org
An approximate binary-black-hole metric
An approximate solution to Einstein's equations representing two
widely-separated non-rotating black holes in a circular orbit is constructed by
matching a post-Newtonian metric to two perturbed Schwarzschild metrics. The
spacetime metric is presented in a single coordinate system valid up to the
apparent horizons of the black holes. This metric could be useful in numerical
simulations of binary black holes. Initial data extracted from this metric have
the advantages of being linked to the early inspiral phase of the binary
system, and of not containing spurious gravitational waves.Comment: 20 pages, 1 figure; some changes in Sec. IV B,C and Sec.
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