2,222 research outputs found
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
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
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
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
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
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.
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
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