1,752 research outputs found
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
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 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-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 of the third post-Newtonian gravitational wave generation of two point masses
Continuing previous work on the 3PN-accurate gravitational wave generation
from point particle binaries, we obtain the binary's 3PN mass-type quadrupole
and dipole moments for general (not necessarily circular) orbits in harmonic
coordinates. The final expressions are given in terms of their ``core'' parts,
resulting from the application of the pure Hadamard-Schwartz (pHS) self-field
regularization scheme, and augmented by an ``ambiguous'' part. In the case of
the 3PN quadrupole we find three ambiguity parameters, xi, kappa and zeta, but
only one for the 3PN dipole, in the form of the particular combination
xi+kappa. Requiring that the dipole moment agree with the center-of-mass
position deduced from the 3PN equations of motion in harmonic coordinates
yields the relation xi+kappa=-9871/9240. Our results will form the basis of the
complete calculation of the 3PN radiation field of compact binaries by means of
dimensional regularization.Comment: 33 pages, to appear in Phys. Rev.
Testing Approximations of Thermal Effects in Neutron Star Merger Simulations
We perform three-dimensional relativistic hydrodynamical calculations of
neutron star mergers to assess the reliability of an approximate treatment of
thermal effects in such simulations by combining an ideal-gas component with
zero-temperature, micro-physical equations of state. To this end we compare the
results of simulations that make this approximation to the outcome of models
with a consistent treatment of thermal effects in the equation of state. In
particular we focus on the implications for observable consequences of merger
events like the gravitational-wave signal. It is found that the characteristic
gravitational-wave oscillation frequencies of the post-merger remnant differ by
about 50 to 250 Hz (corresponding to frequency shifts of 2 to 8 per cent)
depending on the equation of state and the choice of the characteristic index
of the ideal-gas component. In addition, the delay time to black hole collapse
of the merger remnant as well as the amount of matter remaining outside the
black hole after its formation are sensitive to the description of thermal
effects.Comment: 10 pages, 6 figures, 9 eps files; revised with minor additions due to
referee comments; accepted by Phys.Rev.
Gravitational Recoil during Binary Black Hole Coalescence using the Effective One Body Approach
Using the Effective One Body approach, that includes nonperturbative resummed
estimates for the damping and conservative parts of the compact binary
dynamics, we compute the recoil during the late inspiral and the subsequent
plunge of non-spinning black holes of comparable masses moving in
quasi-circular orbits. Further, using a prescription that smoothly connects the
plunge phase to a perturbed single black hole, we obtain an estimate for the
total recoil associated with the binary black hole coalescence. We show that
the crucial physical feature which determines the magnitude of the terminal
recoil is the presence of a ``burst'' of linear momentum flux emitted slightly
before coalescence. When using the most natural expression for the linear
momentum flux during the plunge, together with a Taylor-expanded
correction factor, we find that the maximum value of the terminal recoil is
km/s and occurs for a mass ratio . We comment,
however, on the fact that the above `best bet estimate' is subject to strong
uncertainties because the location and amplitude of the crucial peak of linear
momentum flux happens at a moment during the plunge where most of the
simplifying analytical assumptions underlying the Effective One Body approach
are no longer justified. Changing the analytical way of estimating the linear
momentum flux, we find maximum recoils that range between 49 and 172 km/s.
(Abridged)Comment: 46 pages, new figures and discussions, to appear 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
Gravitational radiation from compact binary systems: gravitational waveforms and energy loss to second post-Newtonian order
We derive the gravitational waveform and gravitational-wave energy flux
generated by a binary star system of compact objects (neutron stars or black
holes), accurate through second post-Newtonian order () beyond the lowest-order quadrupole approximation. We cast the
Einstein equations into the form of a flat-spacetime wave equation together
with a harmonic gauge condition, and solve it formally as a retarded integral
over the past null cone of the chosen field point. The part of this integral
that involves the matter sources and the near-zone gravitational field is
evaluated in terms of multipole moments using standard techniques; the
remainder of the retarded integral, extending over the radiation zone, is
evaluated in a novel way. The result is a manifestly convergent and finite
procedure for calculating gravitational radiation to arbitrary orders in a
post-Newtonian expansion. Through second post-Newtonian order, the radiation is
also shown to propagate toward the observer along true null rays of the
asymptotically Schwarzschild spacetime, despite having been derived using flat
spacetime wave equations. The method cures defects that plagued previous
``brute- force'' slow-motion approaches to the generation of gravitational
radiation, and yields results that agree perfectly with those recently obtained
by a mixed post-Minkowskian post-Newtonian method. We display explicit formulae
for the gravitational waveform and the energy flux for two-body systems, both
in arbitrary orbits and in circular orbits. In an appendix, we extend the
formalism to bodies with finite spatial extent, and derive the spin corrections
to the waveform and energy loss.Comment: 59 pages ReVTeX; Physical Review D, in press; figures available on
request to [email protected]
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