Stable radiation-controlling boundary conditions for the generalized harmonic Einstein equations

This paper is concerned with the initial-boundary value problem for the Einstein equations in a first-order generalized harmonic formulation. We impose boundary conditions that preserve the constraints and control the incoming gravitational radiation by prescribing data for the incoming fields of the Weyl tensor. High-frequency perturbations about any given spacetime (including a shift vector with subluminal normal component) are analyzed using the Fourier-Laplace technique. We show that the system is boundary-stable. In addition, we develop a criterion that can be used to detect weak instabilities with polynomial time dependence, and we show that our system does not suffer from such instabilities. A numerical robust stability test supports our claim that the initial-boundary value problem is most likely to be well-posed even if nonzero initial and source data are included.Comment: 27 pages, 4 figures; more numerical results and references added, several minor amendments; version accepted for publication in Class. Quantum Gra

Comparison of high-accuracy numerical simulations of black-hole binaries with stationary phase post-Newtonian template waveforms for Initial and Advanced LIGO

We study the effectiveness of stationary-phase approximated post-Newtonian waveforms currently used by ground-based gravitational-wave detectors to search for the coalescence of binary black holes by comparing them to an accurate waveform obtained from numerical simulation of an equal-mass non-spinning binary black hole inspiral, merger and ringdown. We perform this study for the Initial- and Advanced-LIGO detectors. We find that overlaps between the templates and signal can be improved by integrating the match filter to higher frequencies than used currently. We propose simple analytic frequency cutoffs for both Initial and Advanced LIGO, which achieve nearly optimal matches, and can easily be extended to unequal-mass, spinning systems. We also find that templates that include terms in the phase evolution up to 3.5 pN order are nearly always better, and rarely significantly worse, than 2.0 pN templates currently in use. For Initial LIGO we recommend a strategy using templates that include a recently introduced pseudo-4.0 pN term in the low-mass (M \leq 35 \MSun) region, and 3.5 pN templates allowing unphysical values of the symmetric reduced mass $\eta$ above this. This strategy always achieves overlaps within 0.3% of the optimum, for the data used here. For Advanced LIGO we recommend a strategy using 3.5 pN templates up to M=12 \MSun, 2.0 pN templates up to M=21 \MSun, pseudo-4.0 pN templates up to 65 \MSun, and 3.5 pN templates with unphysical $\eta$ for higher masses. This strategy always achieves overlaps within 0.7% of the optimum for Advanced LIGO.Comment: 20 pages, 11 figures. Presented at NRDA 200

Testing gravitational-wave searches with numerical relativity waveforms: Results from the first Numerical INJection Analysis (NINJA) project

The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational-wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search algorithms using numerically generated waveforms and to foster closer collaboration between the numerical relativity and data analysis communities. We describe the results of the first NINJA analysis which focused on gravitational waveforms from binary black hole coalescence. Ten numerical relativity groups contributed numerical data which were used to generate a set of gravitational-wave signals. These signals were injected into a simulated data set, designed to mimic the response of the Initial LIGO and Virgo gravitational-wave detectors. Nine groups analysed this data using search and parameter-estimation pipelines. Matched filter algorithms, un-modelled-burst searches and Bayesian parameter-estimation and model-selection algorithms were applied to the data. We report the efficiency of these search methods in detecting the numerical waveforms and measuring their parameters. We describe preliminary comparisons between the different search methods and suggest improvements for future NINJA analyses.Comment: 56 pages, 25 figures; various clarifications; accepted to CQ

Exploring new physics frontiers through numerical relativity

The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We review techniques for solving Einstein's equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology