951 research outputs found
Gravity Waves, Chaos, and Spinning Compact Binaries
Spinning compact binaries are shown to be chaotic in the Post-Newtonian
expansion of the two body system. Chaos by definition is the extreme
sensitivity to initial conditions and a consequent inability to predict the
outcome of the evolution. As a result, the spinning pair will have
unpredictable gravitational waveforms during coalescence. This poses a
challenge to future gravity wave observatories which rely on a match between
the data and a theoretical template.Comment: Final version published in PR
Using Full Information When Computing Modes of Post-Newtonian Waveforms From Inspiralling Compact Binaries in Circular Orbit
The increasing sophistication and accuracy of numerical simulations of
compact binaries (especially binary black holes) presents the opportunity to
test the regime in which post-Newtonian (PN) predictions for the emitted
gravitational waves are accurate. In order to confront numerical results with
those of post-Newtonian theory, it is convenient to compare multipolar
decompositions of the two waveforms. It is pointed out here that the individual
modes can be computed to higher post-Newtonian order by examining the radiative
multipole moments of the system, rather than by decomposing the 2.5PN
polarization waveforms. In particular, the dominant (l = 2, m = 2) mode can be
computed to 3PN order. Individual modes are computed to as high a
post-Newtonian order as possible given previous post-Newtonian results.Comment: 15 page
Numerical simulations of neutron star-black hole binaries in the near-equal-mass regime
Simulations of neutron star-black hole (NSBH) binaries generally consider
black holes with masses in the range , where we expect to find
most stellar mass black holes. The existence of lower mass black holes,
however, cannot be theoretically ruled out. Low-mass black holes in binary
systems with a neutron star companion could mimic neutron star-neutron (NSNS)
binaries, as they power similar gravitational wave (GW) and electromagnetic
(EM) signals. To understand the differences and similarities between NSNS
mergers and low-mass NSBH mergers, numerical simulations are required. Here, we
perform a set of simulations of low-mass NSBH mergers, including systems
compatible with GW170817. Our simulations use a composition and temperature
dependent equation of state (DD2) and approximate neutrino transport, but no
magnetic fields. We find that low-mass NSBH mergers produce remnant disks
significantly less massive than previously expected, and consistent with the
post-merger outflow mass inferred from GW170817 for moderately asymmetric mass
ratio. The dynamical ejecta produced by systems compatible with GW170817 is
negligible except if the mass ratio and black hole spin are at the edge of the
allowed parameter space. That dynamical ejecta is cold, neutron-rich, and
surprisingly slow for ejecta produced during the tidal disruption of a neutron
star : . We also find that the final mass of the remnant
black hole is consistent with existing analytical predictions, while the final
spin of that black hole is noticeably larger than expected -- up to for our equal mass case
Evolution systems for non-linear perturbations of background geometries
The formulation of the initial value problem for the Einstein equations is at
the heart of obtaining interesting new solutions using numerical relativity and
still very much under theoretical and applied scrutiny. We develop a
specialised background geometry approach, for systems where there is
non-trivial a priori knowledge about the spacetime under study. The background
three-geometry and associated connection are used to express the ADM evolution
equations in terms of physical non-linear deviations from that background.
Expressing the equations in first order form leads naturally to a system
closely linked to the Einstein-Christoffel system, introduced by Anderson and
York, and sharing its hyperbolicity properties. We illustrate the drastic
alteration of the source structure of the equations, and discuss why this is
likely to be numerically advantageous.Comment: 12 pages, 3 figures, Revtex v3.0. Revised version to appear in
Physical Review
Toward stable 3D numerical evolutions of black-hole spacetimes
Three dimensional (3D) numerical evolutions of static black holes with
excision are presented. These evolutions extend to about 8000M, where M is the
mass of the black hole. This degree of stability is achieved by using
growth-rate estimates to guide the fine tuning of the parameters in a
multi-parameter family of symmetric hyperbolic representations of the Einstein
evolution equations. These evolutions were performed using a fixed gauge in
order to separate the intrinsic stability of the evolution equations from the
effects of stability-enhancing gauge choices.Comment: 4 pages, 5 figures. To appear in Phys. Rev. D. Minor additions to
text for clarification. Added short paragraph about inner boundary dependenc
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
Einstein boundary conditions for the 3+1 Einstein equations
In the 3+1 framework of the Einstein equations for the case of vanishing
shift vector and arbitrary lapse, we calculate explicitly the four boundary
equations arising from the vanishing of the projection of the Einstein tensor
along the normal to the boundary surface of the initial-boundary value problem.
Such conditions take the form of evolution equations along (as opposed to
across) the boundary for certain components of the extrinsic curvature and for
certain space-derivatives of the intrinsic metric. We argue that, in general,
such boundary conditions do not follow necessarily from the evolution equations
and the initial data, but need to be imposed on the boundary values of the
fundamental variables. Using the Einstein-Christoffel formulation, which is
strongly hyperbolic, we show how three of the boundary equations should be used
to prescribe the values of some incoming characteristic fields. Additionally,
we show that the fourth one imposes conditions on some outgoing fields.Comment: Revtex 4, 6 pages, text and references added, typos corrected, to
appear in Phys. Rev.
Reducing orbital eccentricity of precessing black-hole binaries
Building initial conditions for generic binary black-hole evolutions without
initial spurious eccentricity remains a challenge for numerical-relativity
simulations. This problem can be overcome by applying an eccentricity-removal
procedure which consists in evolving the binary for a couple of orbits,
estimating the eccentricity, and then correcting the initial conditions. The
presence of spins can complicate this procedure. As predicted by post-Newtonian
theory, spin-spin interactions and precession prevent the binary from moving
along an adiabatic sequence of spherical orbits, inducing oscillations in the
radial separation and in the orbital frequency. However, spin-induced
oscillations occur at approximately twice the orbital frequency, therefore they
can be distinguished from the initial spurious eccentricity, which occurs at
approximately the orbital frequency. We develop a new removal procedure based
on the derivative of the orbital frequency and find that it is successful in
reducing the eccentricity measured in the orbital frequency to less than 0.0001
when moderate spins are present. We test this new procedure using
numerical-relativity simulations of binary black holes with mass ratios 1.5 and
3, spin magnitude 0.5 and various spin orientations. The numerical simulations
exhibit spin-induced oscillations in the dynamics at approximately twice the
orbital frequency. Oscillations of similar frequency are also visible in the
gravitational-wave phase and frequency of the dominant mode.Comment: 17 pages, 11 figures, fixed typo
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.
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