2,192 research outputs found
On the structure of the post-Newtonian expansion in general relativity
In the continuation of a preceding work, we derive a new expression for the
metric in the near zone of an isolated matter system in post-Newtonian
approximations of general relativity. The post-Newtonian metric, a solution of
the field equations in harmonic coordinates, is formally valid up to any order,
and is cast in the form of a particular solution of the wave equation, plus a
specific homogeneous solution which ensures the asymptotic matching to the
multipolar expansion of the gravitational field in the exterior of the system.
The new form provides some insights on the structure of the post-Newtonian
expansion in general relativity and the gravitational radiation reaction terms
therein.Comment: 22 pages, to appear in Phys. Rev.
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.
Testing post-Newtonian theory with gravitational wave observations
The Laser Interferometric Space Antenna (LISA) will observe supermassive
black hole binary mergers with amplitude signal-to-noise ratio of several
thousands. We investigate the extent to which such observations afford
high-precision tests of Einstein's gravity. We show that LISA provides a unique
opportunity to probe the non-linear structure of post-Newtonian theory both in
the context of general relativity and its alternatives.Comment: 9 pages, 2 figure
Dimensional regularization of the third post-Newtonian gravitational wave generation from two point masses
Dimensional regularization is applied to the computation of the gravitational
wave field generated by compact binaries at the third post-Newtonian (3PN)
approximation. We generalize the wave generation formalism from isolated
post-Newtonian matter systems to d spatial dimensions, and apply it to point
masses (without spins), modelled by delta-function singularities. We find that
the quadrupole moment of point-particle binaries in harmonic coordinates
contains a pole when epsilon = d-3 -> 0 at the 3PN order. It is proved that the
pole can be renormalized away by means of the same shifts of the particle
world-lines as in our recent derivation of the 3PN equations of motion. The
resulting renormalized (finite when epsilon -> 0) quadrupole moment leads to
unique values for the ambiguity parameters xi, kappa and zeta, which were
introduced in previous computations using Hadamard's regularization. Several
checks of these values are presented. These results complete the derivation of
the gravitational waves emitted by inspiralling compact binaries up to the
3.5PN level of accuracy which is needed for detection and analysis of the
signals in the gravitational-wave antennas LIGO/VIRGO and LISA.Comment: 60 pages, LaTeX 2e, REVTeX 4, 10 PostScript files (1 figure and 9
Young tableaux used in the text
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
Multipole expansion at the level of the action
Sources of long wavelength radiation are naturally described by an effective
field theory (EFT) which takes the form of a multipole expansion. Its action is
given by a derivative expansion where higher order terms are suppressed by
powers of the ratio of the size of the source over the wavelength. In order to
determine the Wilson coefficients of the EFT, i.e. the multipole moments, one
needs the mapping between a linear source term action and the multipole
expansion form of the action of the EFT. In this paper we perform the multipole
expansion to all orders by Taylor expanding the field in the source term and
then decomposing the action into symmetric trace free tensors which form
irreducible representations of the rotation group. We work at the level of the
action, and we obtain the action to all orders in the multipole expansion and
the exact expressions for the multipole moments for a scalar field,
electromagnetism and linearized gravity. Our results for the latter two cases
are manifestly gauge invariant. We also give expressions for the energy flux
and the (gauge dependent) radiation field to all orders in the multipole
expansion. The results for linearized gravity are a component of the EFT
framework NRGR and will greatly simplify future calculations of gravitational
wave observables in the radiation sector of NRGR.Comment: 39 pages, some typos corrected, published versio
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
The dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant
We derive the conservative part of the Lagrangian and the energy of a
gravitationally bound two-body system at fourth post-Newtonian order, up to
terms quadratic in the Newton constant. We also show that such terms are
compatible with Lorentz invariance and we write an ansatz for the
center-of-mass position. The remaining terms carrying higher powers of the
Newton constant are currently under investigation.Comment: 24 pages, 2 figures. Typos in formulae corrected, references added,
more comments in the conclusion in v
Post-Newtonian Gravitational Radiation
1 Introduction 2 Multipole Decomposition 3 Source Multipole Moments 4
Post-Minkowskian Approximation 5 Radiative Multipole Moments 6 Post-Newtonian
Approximation 7 Point-Particles 8 ConclusionComment: 46 pages, in Einstein's Field Equations and Their Physical
Implications, B. Schmidt (Ed.), Lecture Notes in Physics, Springe
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