12 research outputs found
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 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 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