7,541 research outputs found
Spherical harmonic modes of 5.5 post-Newtonian gravitational wave polarizations and associated factorized resummed waveforms for a particle in circular orbit around a Schwarzschild black hol
Recent breakthroughs in numerical relativity enable one to examine the
validity of the post-Newtonian expansion in the late stages of inspiral. For
the comparison between post-Newtonian (PN) expansion and numerical simulations,
the waveforms in terms of the spin-weighted spherical harmonics are more useful
than the plus and cross polarizations, which are used for data analysis of
gravitational waves. Factorized resummed waveforms achieve better agreement
with numerical results than the conventional Taylor expanded post-Newtonian
waveforms. In this paper, we revisit the post-Newtonian expansion of
gravitational waves for a test-particle of mass \m in circular orbit of
radius around a Schwarzschild black hole of mass and derive the
spherical harmonic components associated with the gravitational wave
polarizations up to order beyond Newtonian. Using the more accurate
's computed in this work, we provide the more complete set of
associated 's and 's that form important bricks
in the factorized resummation of waveforms with potential applications for the
construction of further improved waveforms for prototypical compact binary
sources in the future. We also provide ready-to-use expressions of the 5.5PN
gravitational waves polarizations and in the test-particle
limit for gravitational wave data analysis applications. Additionally, we
provide closed analytical expressions for 2.5PN , 2PN and 3PN , for general multipolar orders and in
the test-particle limit. Finally, we also examine the implications of the
present analysis for compact binary sources in Laser Interferometer Space
Antenna.Comment: 42 pages, 2 figures, match with accepted version by PR
Surface-integral expressions for the multipole moments of post-Newtonian sources and the boosted Schwarzschild solution
New expressions for the multipole moments of an isolated post-Newtonian
source, in the form of surface integrals in the outer near-zone, are derived.
As an application we compute the ``source'' quadrupole moment of a
Schwarzschild solution boosted to uniform velocity, at the third post-Newtonian
(3PN) order. We show that the consideration of this boosted Schwarzschild
solution (BSS) is enough to uniquely determine one of the ambiguity parameters
in the recent computation of the gravitational wave generation by compact
binaries at 3PN order: zeta=-7/33. We argue that this value is the only one for
which the Poincar\'e invariance of the 3PN wave generation formalism is
realized. As a check, we confirm the value of zeta by a different method, based
on the far-zone expansion of the BSS at fixed retarded time, and a calculation
of the relevant non-linear multipole interactions in the external metric at the
3PN order.Comment: 30 pages, submitted to Classical and Quantum Gravit
Gravitational waves from inspiralling compact binaries: Energy flux to third post-Newtonian order
The multipolar-post-Minkowskian approach to gravitational radiation is
applied to the problem of the generation of waves by the compact binary
inspiral. We investigate specifically the third post-Newtonian (3PN)
approximation in the total energy flux. The new results are the computation of
the mass quadrupole moment of the binary to the 3PN order, and the current
quadrupole and mass octupole to the 2PN order. Wave tails and tails of tails in
the far zone are included up to the 3.5PN order. The recently derived 3PN
equations of binary motion are used to compute the time-derivatives of the
moments. We find perfect agreement to the 3.5PN order with perturbation
calculations of black holes in the test-mass limit for one body. Technical
inputs in our computation include a model of point particles for describing the
compact objects, and the Hadamard self-field regularization. Because of a
physical incompleteness of the Hadamard regularization at the 3PN order, the
energy flux depends on one unknown physical parameter, which is a combination
of a parameter \lambda in the equations of motion, and a new parameter \theta
coming from the quadrupole moment.Comment: 69 pages, version which includes the correction of an Erratum to be
published in Phys. Rev. D (2005
Second post-Newtonian gravitational radiation reaction for two-body systems: Nonspinning bodies
Starting from the recently obtained 2PN accurate forms of the energy and
angular momentum fluxes from inspiralling compact binaries, we deduce the
gravitational radiation reaction to 2PN order beyond the quadrupole
approximation - 4.5PN terms in the equation of motion - using the refined
balance method proposed by Iyer and Will. We explore critically the features of
their construction and illustrate them by contrast to other possible variants.
The equations of motion are valid for general binary orbits and for a class of
coordinate gauges. The limiting cases of circular orbits and radial infall are
also discussed.Comment: 38 pages, REVTeX, no figures, to appear in Phys. Rev.
Improved filters for gravitational waves from inspiraling compact binaries
The order of the post-Newtonian expansion needed to extract in a reliable and accurate manner the fully general relativistic gravitational wave signal from inspiraling compact binaries is explored. A class of approximate wave forms, called P-approximants, is constructed based on the following two inputs: (a) the introduction of two new energy-type and flux-type functions e(v) and f(v), respectively, (b) the systematic use of the Padé approximation for constructing successive approximants of e(v) and f(v). The new P-approximants are not only more effectual (larger overlaps) and more faithful (smaller biases) than the standard Taylor approximants, but also converge faster and monotonically. The presently available (v/c)^5-accurate post-Newtonian results can be used to construct P-approximate wave forms that provide overlaps with the exact wave form larger than 96.5%, implying that more than 90% of potential events can be detected with the aid of P-approximants as opposed to a mere 10–15 % that would be detectable using standard post-Newtonian approximants
Post-Newtonian prediction for the (2,2) mode of the gravitational wave emitted by compact binaries
We present our 3.5PN computation of the (2,2) mode of the gravitational wave
amplitude emitted by compact binaries, on quasi-circular orbits and in the
absence of spins. We use the multipolar post-Newtonian wave generation
formalism, extending and building on previous works which computed the 3PN
order. This calculation required the extension of the multipolar
post-Minkowskian algorithm, as well as the computation of the mass source
quadrupole at 3.5PN order. Our result will allow more accurate comparisons to
numerical relativity, and is a first step towards the computation of the full
3.5PN waveform amplitude, which would improve the estimation of the source
parameters by gravitational wave detectors.Comment: 5 pages; proceeding of the 9th LISA Symposium, Pari
The third and a half post-Newtonian gravitational wave quadrupole mode for quasi-circular inspiralling compact binaries
We compute the quadrupole mode of the gravitational waveform of inspiralling
compact binaries at the third and a half post-Newtonian (3.5PN) approximation
of general relativity. The computation is performed using the multipolar
post-Newtonian formalism, and restricted to binaries without spins moving on
quasi-circular orbits. The new inputs mainly include the 3.5PN terms in the
mass quadrupole moment of the source, and the control of required subdominant
corrections to the contributions of hereditary integrals (tails and non-linear
memory effect). The result is given in the form of the quadrupolar mode (2,2)
in a spin-weighted spherical harmonic decomposition of the waveform, and may be
used for comparison with the counterpart quantity computed in numerical
relativity. It is a step towards the computation of the full 3.5PN waveform,
whose knowledge is expected to reduce the errors on the location parameters of
the source.Comment: 19 pages, 1 figure; minor corrections, including some rephrasing in
the introduction and in section III
Comparison of post-Newtonian templates for extreme mass ratio inspirals
Extreme mass ratio inspirals (EMRIs), the inspirals of compact objects into
supermassive black holes, are important gravitational wave sources for the
Laser Interferometer Space Antenna (LISA). We study the performance of various
post-Newtonian (PN) template families relative to the high precision numerical
waveforms in the context of EMRI parameter estimation with LISA. Expressions
for the time domain waveforms TaylorT1, TaylorT2, TaylorT3, TaylorT4 and
TaylorEt are derived up to 22PN order, i.e ( is the
characteristic velocity of the binary) beyond the Newtonian term, for a test
particle in a circular orbit around a Schwarzschild black hole. The phase
difference between the above 22PN waveform families and numerical waveforms are
evaluated during two-year inspirals for two prototypical EMRI systems with mass
ratios and . We find that the dephases (in radians) for
TaylorT1 and TaylorT2, respectively, are about () and
() for mass ratio (). This suggests that
using 22PN TaylorT1 or TaylorT2 waveforms for parameter estimation of EMRIs
will result in accuracies comparable to numerical waveform accuracy for most of
the LISA parameter space. On the other hand, from the dephase results, we find
that TaylorT3, TaylorT4 and TaylorEt fare relatively poorly as one approaches
the last stable orbit. This implies that, as for comparable mass binaries using
the 3.5PN phase of waveforms, the 22PN TaylorT3 and TaylorEt approximants do
not perform well enough for the EMRIs. The reason underlying the poor
performance of TaylorT3, TaylorT4 and TaylorEt relative to TaylorT1 and
TaylorT2 is finally examined.Comment: 10 page
Gravitational radiation from inspiralling compact binaries completed at the third post-Newtonian order
The gravitational radiation from point particle binaries is computed at the
third post-Newtonian (3PN) approximation of general relativity. Three
previously introduced ambiguity parameters, coming from the Hadamard self-field
regularization of the 3PN source-type mass quadrupole moment, are consistently
determined by means of dimensional regularization, and proved to have the
values xi = -9871/9240, kappa = 0 and zeta = -7/33. These results complete the
derivation of the general relativistic prediction for compact binary inspiral
up to 3.5PN order, and should be of use for searching and deciphering the
signals in the current network of gravitational wave detectors.Comment: 4 pages in 2-column format, LaTeX 2e, REVTeX 4, no figur
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