7 research outputs found
Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme
A numerical solution scheme for the Einstein field equations based on
generalized harmonic coordinates is described, focusing on details not provided
before in the literature and that are of particular relevance to the binary
black hole problem. This includes demonstrations of the effectiveness of
constraint damping, and how the time slicing can be controlled through the use
of a source function evolution equation. In addition, some results from an
ongoing study of binary black hole coalescence, where the black holes are
formed via scalar field collapse, are shown. Scalar fields offer a convenient
route to exploring certain aspects of black hole interactions, and one
interesting, though tentative suggestion from this early study is that behavior
reminiscent of "zoom-whirl" orbits in particle trajectories is also present in
the merger of equal mass, non-spinning binaries, with appropriately fine-tuned
initial conditions.Comment: 16 pages, 14 figures; replaced with published versio
Are moving punctures equivalent to moving black holes?
When simulating the inspiral and coalescence of a binary black-hole system,
special care needs to be taken in handling the singularities. Two main
techniques are used in numerical-relativity simulations: A first and more
traditional one ``excises'' a spatial neighbourhood of the singularity from the
numerical grid on each spacelike hypersurface. A second and more recent one,
instead, begins with a ``puncture'' solution and then evolves the full
3-metric, including the singular point. In the continuum limit, excision is
justified by the light-cone structure of the Einstein equations and, in
practice, can give accurate numerical solutions when suitable discretizations
are used. However, because the field variables are non-differentiable at the
puncture, there is no proof that the moving-punctures technique is correct,
particularly in the discrete case. To investigate this question we use both
techniques to evolve a binary system of equal-mass non-spinning black holes. We
compare the evolution of two curvature 4-scalars with proper time along the
invariantly-defined worldline midway between the two black holes, using
Richardson extrapolation to reduce the influence of finite-difference
truncation errors. We find that the excision and moving-punctures evolutions
produce the same invariants along that worldline, and thus the same spacetimes
throughout that worldline's causal past. This provides convincing evidence that
moving-punctures are indeed equivalent to moving black holes.Comment: 4 pages, 3 eps color figures; v2 = major revisions to introduction &
conclusions based on referee comments, but no change in analysis or result
The Current Status of Binary Black Hole Simulations in Numerical Relativity
Since the breakthroughs in 2005 which have led to long term stable solutions
of the binary black hole problem in numerical relativity, much progress has
been made. I present here a short summary of the state of the field, including
the capabilities of numerical relativity codes, recent physical results
obtained from simulations, and improvements to the methods used to evolve and
analyse binary black hole spacetimes.Comment: 14 pages; minor changes and corrections in response to referee
Status of NINJA: the Numerical INJection Analysis project
The 2008 NRDA conference introduced the Numerical INJection Analysis project (NINJA), a new collaborative effort between the numerical relativity community and the data analysis community. NINJA focuses on modeling and searching for gravitational wave signatures from the coalescence of binary system of compact objects. We review the scope of this collaboration and the components of the first NINJA project, where numerical relativity groups shared waveforms and data analysis teams applied various techniques to detect them when embedded in colored Gaussian noise
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
From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
This article reviews some aspects in the current relationship between
mathematical and numerical General Relativity. Focus is placed on the
description of isolated systems, with a particular emphasis on recent
developments in the study of black holes. Ideas concerning asymptotic flatness,
the initial value problem, the constraint equations, evolution formalisms,
geometric inequalities and quasi-local black hole horizons are discussed on the
light of the interaction between numerical and mathematical relativists.Comment: Topical review commissioned by Classical and Quantum Gravity.
Discussion inspired by the workshop "From Geometry to Numerics" (Paris, 20-24
November, 2006), part of the "General Relativity Trimester" at the Institut
Henri Poincare (Fall 2006). Comments and references added. Typos corrected.
Submitted to Classical and Quantum Gravit
Characteristic Evolution and Matching
I review the development of numerical evolution codes for general relativity
based upon the characteristic initial value problem. Progress in characteristic
evolution is traced from the early stage of 1D feasibility studies to 2D
axisymmetric codes that accurately simulate the oscillations and gravitational
collapse of relativistic stars and to current 3D codes that provide pieces of a
binary black hole spacetime. Cauchy codes have now been successful at
simulating all aspects of the binary black hole problem inside an artificially
constructed outer boundary. A prime application of characteristic evolution is
to extend such simulations to null infinity where the waveform from the binary
inspiral and merger can be unambiguously computed. This has now been
accomplished by Cauchy-characteristic extraction, where data for the
characteristic evolution is supplied by Cauchy data on an extraction worldtube
inside the artificial outer boundary. The ultimate application of
characteristic evolution is to eliminate the role of this outer boundary by
constructing a global solution via Cauchy-characteristic matching. Progress in
this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note:
updated version of arXiv:gr-qc/050809