1,423 research outputs found
From the self-force problem to the Radiation reaction formula
We review a recent theoretical progress in the so-called self-force problem
of a general relativistic two-body system. Although a two-body system in
Newtonian gravity is a very simple problem, some fundamental issues are
involved in relativistic gravity. Besides, because of recent projects for
gravitational wave detection, it comes to be possible to see those phenomena
directly via gravitational waves, and the self-force problem becomes one of
urgent and highly-motivated problems in general relativity. Roughly speaking,
there are two approaches to investigate this problem; the so-called
post-Newtonian approximation, and a black hole perturbation.
In this paper, we review a theoretical progress in the self-force problem
using a black hole perturbation. Although the self-force problem seems to be
just a problem to calculate a self-force, we discuss that the real problem is
to define a gauge invariant concept of a motion in a gauge dependent metric
perturbation.Comment: a special issue for Classical and Quantum Gravity, a review article
of Capra Ranch Meeting
Non-precessional spin-orbit effects on gravitational waves from inspiraling compact binaries to second post-Newtonian order
We derive all second post-Newtonian (2PN), non-precessional effects of spin-
orbit coupling on the gravitational wave forms emitted by an inspiraling binary
composed of spinning, compact bodies in a quasicircular orbit. Previous post-
Newtonian calculations of spin-orbit effects (at 1.5PN order) relied on a fluid
description of the spinning bodies. We simplify the calculations by introducing
into post-Newtonian theory a delta-function description of the influence of the
spins on the bodies' energy-momentum tensor. This description was recently used
by Mino, Shibata, and Tanaka (MST) in Teukolsky-formalism analyses of particles
orbiting massive black holes, and is based on prior work by Dixon. We compute
the 2PN contributions to the wave forms by combining the MST energy-momentum
tensor with the formalism of Blanchet, Damour, and Iyer for evaluating the
binary's radiative multipoles, and with the well-known 1.5PN order equations of
motion for the binary. Our results contribute at 2PN order only to the
amplitudes of the wave forms. The secular evolution of the wave forms' phase,
the quantity most accurately measurable by LIGO, is not affected by our results
until 2.5PN order, at which point other spin-orbit effects also come into play.
We plan to evaluate the entire 2.5PN spin-orbit contribution to the secular
phase evolution in a future paper, using the techniques of this paper.Comment: 11 pages, submitted to Phys. Rev.
Pragmatic approach to gravitational radiation reaction in binary black holes
We study the relativistic orbit of binary black holes in systems with small
mass ratio. The trajectory of the smaller object (another black hole or a
neutron star), represented as a particle, is determined by the geodesic
equation on the perturbed massive black hole spacetime. The particle itself
generates the gravitational perturbations leading to a problem that needs
regularization. Here we study perturbations around a Schwarzschild black hole
using Moncrief's gauge invariant formalism. We decompose the perturbations into
multipoles to show that all metric coefficients are at the
location of the particle. Summing over , to reconstruct the full metric,
gives a formally divergent result. We succeed in bringing this sum to a
generalized Riemann's function regularization scheme and show that this
is tantamount to subtract the piece to each multipole. We
explicitly carry out this regularization and numerically compute the first
order geodesics. Application of this method to general orbits around rotating
black holes would generate accurate templates for gravitational wave laser
interferometric detectors.Comment: 5 pages, 2 figures, improved text and figures. To appear in PR
Radiation reaction and the self-force for a point mass in general relativity
A point particle of mass m moving on a geodesic creates a perturbation h, of
the spacetime metric g, that diverges at the particle. Simple expressions are
given for the singular m/r part of h and its quadrupole distortion caused by
the spacetime. Subtracting these from h leaves a remainder h^R that is C^1. The
self-force on the particle from its own gravitational field corrects the
worldline at O(m) to be a geodesic of g+h^R. For the case that the particle is
a small non-rotating black hole, an approximate solution to the Einstein
equations is given with error of O(m^2) as m approaches 0.Comment: 4 pages, RevTe
Second post-Newtonian gravitational wave polarizations for compact binaries in elliptical orbits
The second post-Newtonian (2PN) contribution to the `plus' and `cross'
gravitational wave polarizations associated with gravitational radiation from
non-spinning, compact binaries moving in elliptic orbits is computed. The
computation starts from our earlier results on 2PN generation, crucially
employs the 2PN accurate generalized quasi-Keplerian parametrization of
elliptic orbits by Damour, Sch\"afer and Wex and provides 2PN accurate
expressions modulo the tail terms for gravitational wave polarizations
incorporating effects of eccentricity and periastron precession.Comment: 40 pages, 10 figures, To appear in Phys. Rev.
"Peeling property" for linearized gravity in null coordinates
A complete description of the linearized gravitational field on a flat
background is given in terms of gauge-independent quasilocal quantities. This
is an extension of the results from gr-qc/9801068. Asymptotic spherical
quasilocal parameterization of the Weyl field and its relation with Einstein
equations is presented. The field equations are equivalent to the wave
equation. A generalization for Schwarzschild background is developed and the
axial part of gravitational field is fully analyzed. In the case of axial
degree of freedom for linearized gravitational field the corresponding
generalization of the d'Alembert operator is a Regge-Wheeler equation. Finally,
the asymptotics at null infinity is investigated and strong peeling property
for axial waves is proved.Comment: 27 page
A Toy Model for Testing Finite Element Methods to Simulate Extreme-Mass-Ratio Binary Systems
Extreme mass ratio binary systems, binaries involving stellar mass objects
orbiting massive black holes, are considered to be a primary source of
gravitational radiation to be detected by the space-based interferometer LISA.
The numerical modelling of these binary systems is extremely challenging
because the scales involved expand over several orders of magnitude. One needs
to handle large wavelength scales comparable to the size of the massive black
hole and, at the same time, to resolve the scales in the vicinity of the small
companion where radiation reaction effects play a crucial role. Adaptive finite
element methods, in which quantitative control of errors is achieved
automatically by finite element mesh adaptivity based on posteriori error
estimation, are a natural choice that has great potential for achieving the
high level of adaptivity required in these simulations. To demonstrate this, we
present the results of simulations of a toy model, consisting of a point-like
source orbiting a black hole under the action of a scalar gravitational field.Comment: 29 pages, 37 figures. RevTeX 4.0. Minor changes to match the
published versio
Post-Newtonian Gravitational Radiation and Equations of Motion via Direct Integration of the Relaxed Einstein Equations. I. Foundations
We present a self-contained framework called Direct Integration of the
Relaxed Einstein Equations (DIRE) for calculating equations of motion and
gravitational radiation emission for isolated gravitating systems based on the
post-Newtonian approximation. We cast the Einstein equations into their
``relaxed'' form of a flat-spacetime wave equation together with a harmonic
gauge condition, and solve the equations formally as a retarded integral over
the past null cone of the field point (chosen to be within the near zone when
calculating equations of motion, and in the far zone when calculating
gravitational radiation). The ``inner'' part of this integral(within a sphere
of radius one gravitational wavelength) is approximated in a
slow-motion expansion using standard techniques; the ``outer'' part, extending
over the radiation zone, is evaluated using a null integration variable. We
show generally and explicitly that all contributions to the inner integrals
that depend on cancel corresponding terms from the outer integrals,
and that the outer integrals converge at infinity, subject only to reasonable
assumptions about the past behavior of the source. The method cures defects
that plagued previous ``brute-force'' slow-motion approaches to motion and
gravitational radiation for isolated systems. We detail the procedure for
iterating the solutions in a weak-field, slow-motion approximation, and derive
expressions for the near-zone field through 3.5 post-Newtonian order in terms
of Poisson-like potentials.Comment: 43 pages, RevTeX, 3 figures, submitted to Physical Review
The self-force on a static scalar test-charge outside a Schwarzschild black hole
The finite part of the self-force on a static scalar test-charge outside a
Schwarzschild black hole is zero. By direct construction of Hadamard's
elementary solution, we obtain a closed-form expression for the minimally
coupled scalar field produced by a test-charge held fixed in Schwarzschild
spacetime. Using the closed-form expression, we compute the necessary external
force required to hold the charge stationary. Although the energy associated
with the scalar field contributes to the renormalized mass of the particle (and
thereby its weight), we find there is no additional self-force acting on the
charge. This result is unlike the analogous electrostatic result, where, after
a similar mass renormalization, there remains a finite repulsive self-force
acting on a static electric test-charge outside a Schwarzschild black hole. We
confirm our force calculation using Carter's mass-variation theorem for black
holes. The primary motivation for this calculation is to develop techniques and
formalism for computing all forces - dissipative and non-dissipative - acting
on charges and masses moving in a black-hole spacetime. In the Appendix we
recap the derivation of the closed-form electrostatic potential. We also show
how the closed-form expressions for the fields are related to the infinite
series solutions.Comment: RevTeX, To Appear in Phys. Rev.
Reconstruction of Black Hole Metric Perturbations from Weyl Curvature
Perturbation theory of rotating black holes is usually described in terms of
Weyl scalars and , which each satisfy Teukolsky's complex
master wave equation and respectively represent outgoing and ingoing radiation.
On the other hand metric perturbations of a Kerr hole can be described in terms
of (Hertz-like) potentials in outgoing or ingoing {\it radiation
gauges}. In this paper we relate these potentials to what one actually computes
in perturbation theory, i.e and . We explicitly construct
these relations in the nonrotating limit, preparatory to devising a
corresponding approach for building up the perturbed spacetime of a rotating
black hole. We discuss the application of our procedure to second order
perturbation theory and to the study of radiation reaction effects for a
particle orbiting a massive black hole.Comment: 6 Pages, Revtex
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