17 research outputs found

### Spherical Harmonic Decomposition on a Cubic Grid

A method is described by which a function defined on a cubic grid (as from a
finite difference solution of a partial differential equation) can be resolved
into spherical harmonic components at some fixed radius. This has applications
to the treatment of boundary conditions imposed at radii larger than the size
of the grid, following Abrahams, Rezzola, Rupright et al.(gr-qc/9709082}. In
the method described here, the interpolation of the grid data to the
integration 2-sphere is combined in the same step as the integrations to
extract the spherical harmonic amplitudes, which become sums over grid points.
Coordinates adapted to the integration sphere are not needed.Comment: 5 pages, LaTeX uses cjour.cls (supplied

### Cauchy-perturbative matching and outer boundary conditions: Methods and tests

We present a new method of extracting gravitational radiation from three-dimensional numerical relativity codes and providing outer boundary conditions. Our approach matches the solution of a Cauchy evolution of Einstein's equations to a set of one-dimensional linear wave equations on a curved background. We illustrate the mathematical properties of our approach and discuss a numerical module we have constructed for this purpose. This module implements the perturbative matching approach in connection with a generic three-dimensional numerical relativity simulation. Tests of its accuracy and second-order convergence are presented with analytic linear wave data

### Cauchy-perturbative matching and outer boundary conditions: computational studies

We present results from a new technique which allows extraction of
gravitational radiation information from a generic three-dimensional numerical
relativity code and provides stable outer boundary conditions. In our approach
we match the solution of a Cauchy evolution of the nonlinear Einstein field
equations to a set of one-dimensional linear equations obtained through
perturbation techniques over a curved background. We discuss the validity of
this approach in the case of linear and mildly nonlinear gravitational waves
and show how a numerical module developed for this purpose is able to provide
an accurate and numerically convergent description of the gravitational wave
propagation and a stable numerical evolution.Comment: 20 pages, RevTe

### Cauchy-perturbative matching and outer boundary conditions I: Methods and tests

We present a new method of extracting gravitational radiation from
three-dimensional numerical relativity codes and providing outer boundary
conditions. Our approach matches the solution of a Cauchy evolution of
Einstein's equations to a set of one-dimensional linear wave equations on a
curved background. We illustrate the mathematical properties of our approach
and discuss a numerical module we have constructed for this purpose. This
module implements the perturbative matching approach in connection with a
generic three-dimensional numerical relativity simulation. Tests of its
accuracy and second-order convergence are presented with analytic linear wave
data.Comment: 13 pages, 6 figures, RevTe

### Boosted three-dimensional black-hole evolutions with singularity excision

Binary black hole interactions provide potentially the strongest source of
gravitational radiation for detectors currently under development. We present
some results from the Binary Black Hole Grand Challenge Alliance three-
dimensional Cauchy evolution module. These constitute essential steps towards
modeling such interactions and predicting gravitational radiation waveforms. We
report on single black hole evolutions and the first successful demonstration
of a black hole moving freely through a three-dimensional computational grid
via a Cauchy evolution: a hole moving ~6M at 0.1c during a total evolution of
duration ~60M

### Gravitational wave extraction and outer boundary conditions by perturbative matching

We present a method for extracting gravitational radiation from a
three-dimensional numerical relativity simulation and, using the extracted
data, to provide outer boundary conditions. The method treats dynamical
gravitational variables as nonspherical perturbations of Schwarzschild
geometry. We discuss a code which implements this method and present results of
tests which have been performed with a three dimensional numerical relativity
code

### Stable characteristic evolution of generic 3-dimensional single-black-hole spacetimes

We report new results which establish that the accurate 3-dimensional
numerical simulation of generic single-black-hole spacetimes has been achieved
by characteristic evolution with unlimited long term stability. Our results
cover a selection of distorted, moving and spinning single black holes, with
evolution times up to 60,000M.Comment: 4 pages, 3 figure

### Three-dimensional general relativistic hydrodynamics II: long-term dynamics of single relativistic stars

This is the second in a series of papers on the construction and validation
of a three-dimensional code for the solution of the coupled system of the
Einstein equations and of the general relativistic hydrodynamic equations, and
on the application of this code to problems in general relativistic
astrophysics. In particular, we report on the accuracy of our code in the
long-term dynamical evolution of relativistic stars and on some new physics
results obtained in the process of code testing. The tests involve single
non-rotating stars in stable equilibrium, non-rotating stars undergoing radial
and quadrupolar oscillations, non-rotating stars on the unstable branch of the
equilibrium configurations migrating to the stable branch, non-rotating stars
undergoing gravitational collapse to a black hole, and rapidly rotating stars
in stable equilibrium and undergoing quasi-radial oscillations. The numerical
evolutions have been carried out in full general relativity using different
types of polytropic equations of state using either the rest-mass density only,
or the rest-mass density and the internal energy as independent variables. New
variants of the spacetime evolution and new high resolution shock capturing
(HRSC) treatments based on Riemann solvers and slope limiters have been
implemented and the results compared with those obtained from previous methods.
Finally, we have obtained the first eigenfrequencies of rotating stars in full
general relativity and rapid rotation. A long standing problem, such
frequencies have not been obtained by other methods. Overall, and to the best
of our knowledge, the results presented in this paper represent the most
accurate long-term three-dimensional evolutions of relativistic stars available
to date.Comment: 19 pages, 17 figure

### Gravitational wave extraction and outer boundary conditions by perturbative matching

We present a method for extracting gravitational radiation from a three-dimensional numerical relativity simulation and, using the extracted data, to provide outer boundary conditions. The method treats dynamical gravitational variables as nonspherical perturbations of Schwarzschild geometry. We discuss a code which implements this method and present results of tests which have been performed with a three dimensional numerical relativity code