2,032 research outputs found

### Effective action approach to higher-order relativistic tidal interactions in binary systems and their effective one body description

The gravitational-wave signal from inspiralling neutron-star--neutron-star
(or black-hole--neutron-star) binaries will be influenced by tidal coupling in
the system. An important science goal in the gravitational-wave detection of
these systems is to obtain information about the equation of state of neutron
star matter via the measurement of the tidal polarizability parameters of
neutron stars. To extract this piece of information will require to have
accurate analytical descriptions of both the motion and the radiation of
tidally interacting binaries. We improve the analytical description of the late
inspiral dynamics by computing the next-to-next-to-leading order relativistic
correction to the tidal interaction energy. Our calculation is based on an
effective-action approach to tidal interactions, and on its transcription
within the effective-one-body formalism. We find that second-order relativistic
effects (quadratic in the relativistic gravitational potential $u=G(m_1
+m_2)/(c^2 r)$) significantly increase the effective tidal polarizability of
neutron stars by a distance-dependent amplification factor of the form $1 +
\alpha_1 \, u + \alpha_2 \, u^2 +...$ where, say for an equal-mass binary,
$\alpha_1=5/4=1.25$ (as previously known) and $\alpha_2=85/14\simeq6.07143$ (as
determined here for the first time). We argue that higher-order relativistic
effects will lead to further amplification, and we suggest a Pad\'e-type way of
resumming them. We recommend to test our results by comparing
resolution-extrapolated numerical simulations of inspiralling-binary neutron
stars to their effective one body description.Comment: 29 pages, Physical Review D, to appea

### Orbital Tests of Relativistic Gravity using Artificial Satellites

We reexamine non-Einsteinian effects observable in the orbital motion of
low-orbit artificial Earth satellites. The motivations for doing so are
twofold: (i) recent theoretical studies suggest that the correct theory of
gravity might contain a scalar contribution which has been reduced to a small
value by the effect of the cosmological expansion; (ii) presently developed
space technologies should soon give access to a new generation of satellites
endowed with drag-free systems and tracked in three dimensions at the
centimeter level. Our analysis suggests that such data could measure two
independent combinations of the Eddington parameters (beta - 1) and (gamma - 1)
at the 10^-4 level and probe the time variability of Newton's "constant" at the
d(ln G)/dt ~ 10^-13 yr^-1 level. These tests would provide well-needed
complements to the results of the Lunar Laser Ranging experiment, and of the
presently planned experiments aiming at measuring (gamma -1). In view of the
strong demands they make on the level of non- gravitational perturbations,
these tests might require a dedicated mission consisting of an optimized
passive drag-free satellite.Comment: 17 pages, IHES/P/94/22 and CPT-94/P.E.302

### Conservation laws for systems of extended bodies in the first post-Newtonian approximation.

The general form of the global conservation laws for $N$-body systems in the
first post-Newtonian approximation of general relativity is considered. Our
approach applies to the motion of an isolated system of $N$ arbitrarily
composed and shaped, weakly self-gravitating, rotating, deformable bodies and
uses a framework recently introduced by Damour, Soffel and Xu (DSX). We succeed
in showing that seven of the first integrals of the system (total mass-energy,
total dipole mass moment and total linear momentum) can be broken up into a sum
of contributions which can be entirely expressed in terms of the basic
quantities entering the DSX framework: namely, the relativistic individual
multipole moments of the bodies, the relativistic tidal moments experienced by
each body, and the positions and orientations with respect to the global
coordinate system of the local reference frames attached to each body. On the
other hand, the total angular momentum of the system does not seem to be
expressible in such a form due to the unavoidable presence of irreducible
nonlinear gravitational effects.Comment: 18 pages, Revte

### Primordial black hole evolution in tensor-scalar cosmology

A perturbative analysis shows that black holes do not remember the value of
the scalar field $\phi$ at the time they formed if $\phi$ changes in
tensor-scalar cosmology. Moreover, even when the black hole mass in the
Einstein frame is approximately unaffected by the changing of $\phi$, in the
Jordan-Fierz frame the mass increases. This mass increase requires a reanalysis
of the evaporation of primordial black holes in tensor-scalar cosmology. It
also implies that there could have been a significant magnification of the
(Jordan-Fierz frame) mass of primordial black holes.Comment: 4 pages, revte

### Testing gravity to second post-Newtonian order: a field-theory approach

A new, field-theory-based framework for discussing and interpreting tests of
gravity, notably at the second post-Newtonian (2PN) level, is introduced.
Contrary to previous frameworks which attempted at parametrizing any
conceivable deviation from general relativity, we focus on the best motivated
class of models, in which gravity is mediated by a tensor field together with
one or several scalar fields. The 2PN approximation of these
"tensor-multi-scalar" theories is obtained thanks to a diagrammatic expansion
which allows us to compute the Lagrangian describing the motion of N bodies. In
contrast with previous studies which had to introduce many phenomenological
parameters, we find that the 2PN deviations from general relativity can be
fully described by only two new 2PN parameters, epsilon and zeta, beyond the
usual (Eddington) 1PN parameters beta and gamma. It follows from the basic
tenets of field theory, notably the absence of negative-energy excitations,
that (beta-1), epsilon and zeta (as well as any new parameter entering higher
post-Newtonian orders) must tend to zero with (gamma-1). It is also found that
epsilon and zeta do not enter the 2PN equations of motion of light. Therefore,
light-deflection or time-delay experiments cannot probe any theoretically
motivated 2PN deviation from general relativity, but they can give a clean
access to (gamma-1), which is of greatest significance as it measures the basic
coupling strength of matter to the scalar fields. Because of the importance of
self-gravity effects in neutron stars, binary-pulsar experiments are found to
constitute a unique testing ground for the 2PN structure of gravity. A
simplified analysis of four binary pulsars already leads to significant
constraints: |epsilon| < 7x10^-2, |zeta| < 6x10^-3.Comment: 63 pages, 11 figures.ps.tar.gz.uu, REVTeX 3.

### Phasing of gravitational waves from inspiralling eccentric binaries at the third-and-a-half post-Newtonian order

We obtain an efficient description for the dynamics of nonspinning compact
binaries moving in inspiralling eccentric orbits to implement the phasing of
gravitational waves from such binaries at the 3.5 post-Newtonian (PN) order.
Our computation heavily depends on the phasing formalism, presented in [T.
Damour, A. Gopakumar, and B. R. Iyer, Phys. Rev. D \textbf{70}, 064028 (2004)],
and the 3PN accurate generalized quasi-Keplerian parametric solution to the
conservative dynamics of nonspinning compact binaries moving in eccentric
orbits, available in [R.-M. Memmesheimer, A. Gopakumar, and G. Sch\"afer, Phys.
Rev. D \textbf{70}, 104011 (2004)]. The gravitational-wave (GW) polarizations
$h_{+}$ and $h_{\times}$ with 3.5PN accurate phasing should be useful for the
earth-based GW interferometers, current and advanced, if they plan to search
for gravitational waves from inspiralling eccentric binaries. Our results will
be required to do \emph{astrophysics} with the proposed space-based GW
interferometers like LISA, BBO, and DECIGO.Comment: 22 pages including 2 figures; submitted to PR

### Dimensional regularization of the third post-Newtonian dynamics of point particles in harmonic coordinates

Dimensional regularization is used to derive the equations of motion of two
point masses in harmonic coordinates. At the third post-Newtonian (3PN)
approximation, it is found that the dimensionally regularized equations of
motion contain a pole part [proportional to 1/(d-3)] which diverges as the
space dimension d tends to 3. It is proven that the pole part can be
renormalized away by introducing suitable shifts of the two world-lines
representing the point masses, and that the same shifts renormalize away the
pole part of the "bulk" metric tensor g_munu(x). The ensuing, finite
renormalized equations of motion are then found to belong to the general
parametric equations of motion derived by an extended Hadamard regularization
method, and to uniquely determine the heretofore unknown 3PN parameter lambda
to be: lambda = - 1987/3080. This value is fully consistent with the recent
determination of the equivalent 3PN static ambiguity parameter, omega_s = 0, by
a dimensional-regularization derivation of the Hamiltonian in
Arnowitt-Deser-Misner coordinates. Our work provides a new, powerful check of
the consistency of the dimensional regularization method within the context of
the classical gravitational interaction of point particles.Comment: 82 pages, LaTeX 2e, REVTeX 4, 8 PostScript figures, minor changes to
reflect Phys. Rev. D versio

### Parametric derivation of the observable relativistic periastron advance for binary pulsars

We compute the dimensionless relativistic periastron advance parameter $k$,
which is measurable from the timing of relativistic binary pulsars. We employ
for the computation the recently derived Keplerian-type parametric solution to
the post-Newtonian (PN) accurate conservative dynamics of spinning compact
binaries moving in eccentric orbits. The parametric solution and hence the
parameter $k$ are applicable for the cases of \emph{simple precession}, namely,
case (i), the binary consists of equal mass compact objects, having two
arbitrary spins, and case (ii), the binary consists of compact objects of
arbitrary mass, where only one of them is spinning with an arbitrary spin. Our
expression, for the cases considered, is in agreement with a more general
formula for the 2PN accurate $k$, relevant for the relativistic double pulsar
PSR J0737--3039, derived by Damour and Sch\"afer many years ago, using a
different procedure.Comment: 12 pages including 1 figure; submitted to PR

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