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