5,923 research outputs found
Constraint Damping in First-Order Evolution Systems for Numerical Relativity
A new constraint suppressing formulation of the Einstein evolution equations
is presented, generalizing the five-parameter first-order system due to Kidder,
Scheel and Teukolsky (KST). The auxiliary fields, introduced to make the KST
system first-order, are given modified evolution equations designed to drive
constraint violations toward zero. The algebraic structure of the new system is
investigated, showing that the modifications preserve the hyperbolicity of the
fundamental and constraint evolution equations. The evolution of the
constraints for pertubations of flat spacetime is completely analyzed, and all
finite-wavelength constraint modes are shown to decay exponentially when
certain adjustable parameters satisfy appropriate inequalities. Numerical
simulations of a single Schwarzschild black hole are presented, demonstrating
the effectiveness of the new constraint-damping modifications.Comment: 11 pages, 5 figure
Making use of geometrical invariants in black hole collisions
We consider curvature invariants in the context of black hole collision
simulations. In particular, we propose a simple and elegant combination of the
Weyl invariants I and J, the {\sl speciality index} . In the context
of black hole perturbations provides a measure of the size of the
distortions from an ideal Kerr black hole spacetime. Explicit calculations in
well-known examples of axisymmetric black hole collisions demonstrate that this
quantity may serve as a useful tool for predicting in which cases perturbative
dynamics provide an accurate estimate of the radiation waveform and energy.
This makes particularly suited to studying the transition from
nonlinear to linear dynamics and for invariant interpretation of numerical
results.Comment: 4 pages, 3 eps figures, Revte
The Lazarus project: A pragmatic approach to binary black hole evolutions
We present a detailed description of techniques developed to combine 3D
numerical simulations and, subsequently, a single black hole close-limit
approximation. This method has made it possible to compute the first complete
waveforms covering the post-orbital dynamics of a binary black hole system with
the numerical simulation covering the essential non-linear interaction before
the close limit becomes applicable for the late time dynamics. To determine
when close-limit perturbation theory is applicable we apply a combination of
invariant a priori estimates and a posteriori consistency checks of the
robustness of our results against exchange of linear and non-linear treatments
near the interface. Once the numerically modeled binary system reaches a regime
that can be treated as perturbations of the Kerr spacetime, we must
approximately relate the numerical coordinates to the perturbative background
coordinates. We also perform a rotation of a numerically defined tetrad to
asymptotically reproduce the tetrad required in the perturbative treatment. We
can then produce numerical Cauchy data for the close-limit evolution in the
form of the Weyl scalar and its time derivative
with both objects being first order coordinate and tetrad invariant. The
Teukolsky equation in Boyer-Lindquist coordinates is adopted to further
continue the evolution. To illustrate the application of these techniques we
evolve a single Kerr hole and compute the spurious radiation as a measure of
the error of the whole procedure. We also briefly discuss the extension of the
project to make use of improved full numerical evolutions and outline the
approach to a full understanding of astrophysical black hole binary systems
which we can now pursue.Comment: New typos found in the version appeared in PRD. (Mostly found and
collected by Bernard Kelly
On the energy and baseline optimization to study effects related to the ÎŽ-phase (CP-/T-violation) in neutrino oscillations at a neutrino factory
In this paper we discuss the detection of CP- and T-violation effects in the framework of a neutrino factory. We introduce three quantities, which are good discriminants for a non-vanishing complex phase (ÎŽ) in the 3 Ă 3 neutrino mixing matrix: ÎÎŽ, ÎCP and ÎT. We find that these three discriminants (in vacuum) all scale with L/Ev, where L is the baseline and Ev the neutrino energy. Matter effects modify the scaling, but these effects are large enough to spoil the sensitivity only for baselines larger than 5000 km. So, in the hypothesis of constant neutrino factory power (i.e., number of muons inversely proportional to muon energy), the sensitivity on the ÎŽ-phase is independent of the baseline chosen. Specially interesting is the direct measurement of T-violation from the "wrong-sign" electron channel (i.e., the ÎT discriminant), which involves a comparison of the ve â vÎŒ and vÎŒ â ve oscillation rates. However, the vÎŒ â ve measurement requires magnetic discrimination of the electron charge, experimentally very challenging in a neutrino detector. Since the direction of the electron curvature has to be estimated before the start of the electromagnetic shower, low-energy neutrino beams and hence short baselines, are preferred. In this paper we show, as an example, the exclusion regions in the Îm212-ÎŽ plane using the ÎCP and ÎT discriminants for two concrete cases keeping the same L/Ev ratio (730 km/7.5 GeV and 2900 km/30 GeV). We obtain a similar excluded region provided that the electron detection efficiency is âŒ20% and the charge confusion 0.1%. The Îm212 compatible with the LMA solar data can be tested with a flux of 5 Ă 1021 muons. We compare these results with the fit of the visible energy distributions. © 2002 Elsevier Science B.V. All rights reserved
A perturbative solution for gravitational waves in quadratic gravity
We find a gravitational wave solution to the linearized version of quadratic
gravity by adding successive perturbations to the Einstein's linearized field
equations. We show that only the Ricci squared quadratic invariant contributes
to give a different solution of those found in Einstein's general relativity.
The perturbative solution is written as a power series in the
parameter, the coefficient of the Ricci squared term in the quadratic
gravitational action. We also show that, for monochromatic waves of a given
angular frequency , the perturbative solution can be summed out to give
an exact solution to linearized version of quadratic gravity, for
.
This result may lead to implications to the predictions for gravitational
wave backgrounds of cosmological origin.Comment: 9 pages, to appear in CQ
The Yamabe invariant for axially symmetric two Kerr black holes initial data
An explicit 3-dimensional Riemannian metric is constructed which can be
interpreted as the (conformal) sum of two Kerr black holes with aligned angular
momentum. When the separation distance between them is large we prove that this
metric has positive Ricci scalar and hence positive Yamabe invariant. This
metric can be used to construct axially symmetric initial data for two Kerr
black holes with large angular momentum.Comment: 14 pages, 2 figure
The importance of precession in modelling the direction of the final spin from a black-hole merger
The prediction of the spin of the black hole resulting from the merger of a
generic black-hole binary system is of great importance to study the
cosmological evolution of supermassive black holes. Several attempts have been
recently made to model the spin via simple expressions exploiting the results
of numerical-relativity simulations. Here, I first review the derivation of a
formula, proposed in Barausse & Rezzolla, Apj 704 L40, which accurately
predicts the final spin magnitude and direction when applied to binaries with
separations of hundred or thousands of gravitational radii. This makes my
formula particularly suitable for cosmological merger-trees and N-body
simulations, which provide the spins and angular momentum of the two black
holes when their separation is of thousands of gravitational radii. More
importantly, I investigate the physical reason behind the good agreement
between my formula and numerical relativity simulations, and nail it down to
the fact that my formula takes into account the post-Newtonian precession of
the spins and angular momentum in a consistent manner.Comment: 6 pages, 2 figures. Panel added to fig 2, discussion extended to
comply with referee's comments. Version accepted for publication as
proceeding of the 8th Amaldi International Conference on Gravitational Waves,
NYC, 21-26 June 200
Plunge waveforms from inspiralling binary black holes
We study the coalescence of non-spinning binary black holes from near the
innermost stable circular orbit down to the final single rotating black hole.
We use a technique that combines the full numerical approach to solve Einstein
equations, applied in the truly non-linear regime, and linearized perturbation
theory around the final distorted single black hole at later times. We compute
the plunge waveforms which present a non negligible signal lasting for showing early non-linear ringing, and we obtain estimates for the total
gravitational energy and angular momentum radiated.Comment: Corrected typos in the radiated ang momentum and frequenc
Large Merger Recoils and Spin Flips From Generic Black-Hole Binaries
We report the first results from evolutions of a generic black-hole binary,
i.e. a binary containing unequal mass black holes with misaligned spins. Our
configuration, which has a mass ratio of 2:1, consists of an initially
non-spinning hole orbiting a larger, rapidly spinning hole (specific spin a/m =
0.885), with the spin direction oriented -45 degrees with respect to the
orbital plane. We track the inspiral and merger for ~2 orbits and find that the
remnant receives a substantial kick of 454 km/s, more than twice as large as
the maximum kick from non-spinning binaries. The remnant spin direction is
flipped by 103 degrees with respect to the initial spin direction of the larger
hole. We performed a second run with anti-aligned spins, a/m = +-0.5 lying in
the orbital plane that produces a kick of 1830 km/s off the orbital plane. This
value scales to nearly 4000 km/s for maximally spinning holes. Such a large
recoil velocity opens the possibility that a merged binary can be ejected even
from the nucleus of a massive host galaxy.Comment: 4 pages. Accepted for publication in ApJ
Cognitive interviewing as tool for enhancing the accuracy of the interpretation of quantitative findings
This paper contrasts findings from a quantitative survey with those from a cognitive interviewing follow-up investigation on a subset of the same respondents. The data were gathered as part of a larger study to explore measurement error across three modes of data collection, but this paper focuses on the question format experiments rather than the mode effects part of the larger study. Three examples are presented which demonstrate how cognitive interviewing can cast new light on quantitative results by increasing the accuracy of the inferences made. These include instances where: (1) quantitative indicators of poor respondent behaviour (e.g., acquiescence bias on agree/disagree questions) are over-estimates, (2) similar quantitative response distributions across satisfaction and behavioural questions (from a fully-labelled versus end-labelled experiment) imply similar respondent satisficing behaviour, but cognitive interviews show that different response processes are at work and (3) unlikely quantitative findings (from an experiment comparing 3 vs. 7 or 8 response options) could easily be dismissed as due to chance but were instead the result of unforeseen respondent difficulties. The paper concludes with a discussion of the value of using a cognitive interviewing follow-up study as a tool in the interpretation of ambiguous quantitative findings
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