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} ${\cal S}$. In the context of black hole perturbations $\cal S$ 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 ${\cal S}$ 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 $\psi_4$ and its time derivative $\partial_t\psi_4$ 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 δ-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 (δ) in the 3 × 3 neutrino mixing matrix: Δδ, ΔCP and ΔT. 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 δ-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 ΔT discriminant), which involves a comparison of the ve → vμ and vμ → ve oscillation rates. However, the vμ → 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 Δm212-δ plane using the ΔCP and ΔT 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 ∼20% and the charge confusion 0.1%. The Δm212 compatible with the LMA solar data can be tested with a flux of 5 × 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 $\beta$ 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 $\omega$, the perturbative solution can be summed out to give an exact solution to linearized version of quadratic gravity, for $0<\omega<c/\mid\beta\mid^{1/2}$. 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 $t\sim 100M$ 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

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

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