2,326 research outputs found
Gravitational self-force and the effective-one-body formalism between the innermost stable circular orbit and the light ring
We compute the conservative piece of the gravitational self-force (GSF)
acting on a particle of mass m_1 as it moves along an (unstable) circular
geodesic orbit between the innermost stable circular orbit (ISCO) and the light
ring of a Schwarzschild black hole of mass m_2>> m_1. More precisely, we
construct the function h_{uu}(x) = h_{\mu\nu} u^{\mu} u^{\nu} (related to
Detweiler's gauge-invariant "redshift" variable), where h_{\mu\nu} is the
regularized metric perturbation in the Lorenz gauge, u^{\mu} is the
four-velocity of m_1, and x= [Gc^{-3}(m_1+m_2)\Omega]^{2/3} is an invariant
coordinate constructed from the orbital frequency \Omega. In particular, we
explore the behavior of h_{uu} just outside the "light ring" at x=1/3, where
the circular orbit becomes null. Using the recently discovered link between
h_{uu} and the piece a(u), linear in the symmetric mass ratio \nu, of the main
radial potential A(u,\nu) of the Effective One Body (EOB) formalism, we compute
a(u) over the entire domain 0<u<1/3. We find that a(u) diverges at the
light-ring as ~0.25 (1-3u)^{-1/2}, explain the physical origin of this
divergence, and discuss its consequences for the EOB formalism. We construct
accurate global analytic fits for a(u), valid on the entire domain 0<u<1/3 (and
possibly beyond), and give accurate numerical estimates of the values of a(u)
and its first 3 derivatives at the ISCO, as well as the O(\nu) shift in the
ISCO frequency. In previous work we used GSF data on slightly eccentric orbits
to compute a certain linear combination of a(u) and its first two derivatives,
involving also the O(\nu) piece \bar d(u) of a second EOB radial potential
{\bar D}(u,\nu). Combining these results with our present global analytic
representation of a(u), we numerically compute {\bar d}(u)$ on the interval
0<u\leq 1/6.Comment: 44 pages, 8 figures. Extended discussion in Section V and minor
typographical corrections throughout. Version to be published in PR
Conservation laws for systems of extended bodies in the first post-Newtonian approximation.
The general form of the global conservation laws for -body systems in the
first post-Newtonian approximation of general relativity is considered. Our
approach applies to the motion of an isolated system of 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
Introductory lectures on the Effective One Body formalism
The Effective One Body (EOB) formalism is an analytical approach which aims
at providing an accurate description of the motion and radiation of coalescing
binary black holes. We present a brief review of the basic elements of this
approach.Comment: 22 pages, 3 figures, lectures given at the Second ICRANet
Stueckelberg Workshop on Relativistic Field Theories (Pescara, Italy,
September 3-8, 2007); to be published in the International Journal of Modern
Physics
Photon rockets and gravitational radiation
The absence of gravitational radiation in Kinnersley's ``photon rocket''
solution of Einstein's equations is clarified by studying the mathematically
well-defined problem of point-like photon rockets in Minkowski space (i.e.
massive particles emitting null fluid anisotro\-pically and accelerating
because of the recoil). We explicitly compute the (uniquely defined) {\it
linearized} retarded gravitational waves emitted by such objects, which are the
coherent superposition of the gravitational waves generated by the motion of
the massive point-like rocket and of those generated by the energy-momentum
distribution of the photon fluid. In the special case (corresponding to
Kinnersley's solution) where the anisotropy of the photon emission is purely
dipolar we find that the gravitational wave amplitude generated by the
energy-momentum of the photons exactly cancels the usual gravitational
wave amplitude generated by the accelerated motion of the rocket. More general
photon anisotropies would, however, generate genuine gravitational radiation at
infinity. Our explicit calculations show the compatibility between the
non-radiative character of Kinnersley's solution and the currently used
gravitational wave generation formalisms based on post-Minkowskian perturbation
theory.Comment: 21 pages, LATEX, submitted to Class. Quant. Gra
Light deflection by gravitational waves from localized sources
We study the deflection of light (and the redshift, or integrated time delay)
caused by the time-dependent gravitational field generated by a localized
material source lying close to the line of sight. Our calculation explicitly
takes into account the full, near-zone, plus intermediate-zone, plus wave-zone,
retarded gravitational field. Contrary to several recent claims in the
literature, we find that the deflections due to both the wave-zone 1/r
gravitational wave and the intermediate-zone 1/r^2 retarded fields vanish
exactly. The leading total time-dependent deflection caused by a localized
material source, such as a binary system, is proven to be given by the
quasi-static, near-zone quadrupolar piece of the gravitational field, and
therefore to fall off as the inverse cube of the impact parameter.Comment: 12 pages, REVTeX 3.0, no figur
Investigation of wall normal electromagnetic actuator for seawater flow control
Submitted versio
Improved filters for gravitational waves from inspiralling 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 inspiralling 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 Pade 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 O(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.Comment: Latex ([prd,aps,eqsecnum,epsf]{revtex}), 40 pages including 12
encapsulated figures. (The paper, together with all the figures and tables is
available from ftp://carina.astro.cf.ac.uk/pub/incoming/sathya/dis97.uu
The Equivalence Principle and the Constants of Nature
We briefly review the various contexts within which one might address the
issue of ``why'' the dimensionless constants of Nature have the particular
values that they are observed to have. Both the general historical trend, in
physics, of replacing a-priori-given, absolute structures by dynamical
entities, and anthropic considerations, suggest that coupling ``constants''
have a dynamical nature. This hints at the existence of observable violations
of the Equivalence Principle at some level, and motivates the need for improved
tests of the Equivalence Principle.Comment: 12 pages; invited talk at the ISSI Workshop on the Nature of Gravity:
Confronting Theory and Experiment in Space, Bern, Switzerland, 6-10 October
2008; to appear in Space Science Review
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
A Comparison of search templates for gravitational waves from binary inspiral
We compare the performances of the templates defined by three different types
of approaches: traditional post-Newtonian templates (Taylor-approximants),
``resummed'' post-Newtonian templates assuming the adiabatic approximation and
stopping before the plunge (P-approximants), and further ``resummed''
post-Newtonian templates going beyond the adiabatic approximation and
incorporating the plunge with its transition from the inspiral
(Effective-one-body approximants). The signal to noise ratio is significantly
enhanced (mainly because of the inclusion of the plunge signal) by using these
new effective-one-body templates relative to the usual post-Newtonian ones for
binary masses greater than , the most likely sources for initial
laser interferometers. Independently of the question of the plunge signal, the
comparison of the various templates confirms the usefulness of using
resummation methods. The paper also summarizes the key elements of the
construction of various templates and thus can serve as a resource for those
involved in writing inspiral search software.Comment: eta-dependent tail terms corrected after related errata by Blanchet
(2005
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