5,783 research outputs found
Applying black hole perturbation theory to numerically generated spacetimes
Nonspherical perturbation theory has been necessary to understand the meaning
of radiation in spacetimes generated through fully nonlinear numerical
relativity. Recently, perturbation techniques have been found to be successful
for the time evolution of initial data found by nonlinear methods. Anticipating
that such an approach will prove useful in a variety of problems, we give here
both the practical steps, and a discussion of the underlying theory, for taking
numerically generated data on an initial hypersurface as initial value data and
extracting data that can be considered to be nonspherical perturbations.Comment: 14 pages, revtex3.0, 5 figure
Black hole collisions from Brill-Lindquist initial data: predictions of perturbation theory
The Misner initial value solution for two momentarily stationary black holes
has been the focus of much numerical study. We report here analytic results for
an astrophysically similar initial solution, that of Brill and Lindquist (BL).
Results are given from perturbation theory for initially close holes and are
compared with available numerical results. A comparison is made of the
radiation generated from the BL and the Misner initial values, and the physical
meaning is discussed.Comment: 11 pages, revtex3.0, 5 figure
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
There\u27s A Million Heroes in Each Corner of the U.S.A
[Verse 1] Virginia gave us Washington, way back in Sev’nty six Kentucky gave us Lincoln when our boys were in a fix Ohio gave us Grant and Dixie gave us Lee They fought it out and patched it up and made our history If you asked Uncle Sammy who could take their place today He’d rub his chin and with a grin he’d answer in this way.
[Chorus] There’s a million heroes in each corner of the U.S.A. In cities and farms They’ve taken up arms The East and West have sent their best the rest are coming from the land of cotton You can bank on ev’ry loyal Yank to fight till the end of the fray When danger threatens they all rally ‘round That’s why the flag has never touched the ground There’s a million heroes in each corner of the U.S.A.
[Verse 2] Columbus found America the home of peace and rest And Betsy Ross she found a flag to stand each battle test Tho’ heroes of the past have laid away the gun Their spirits live within the hearts of ev’ry native son Our flag is just as clean today as when it first was made each stripe and star a battle scar and still I’m not afraid.
[Chorus
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