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

Waveform propagation in black hole spacetimes: evaluating the quality of numerical solutions

We compute the propagation and scattering of linear gravitational waves off a Schwarzschild black hole using a numerical code which solves a generalization of the Zerilli equation to a three dimensional cartesian coordinate system. Since the solution to this problem is well understood it represents a very good testbed for evaluating our ability to perform three dimensional computations of gravitational waves in spacetimes in which a black hole event horizon is present.Comment: 13 pages, RevTeX, to appear in Phys. Rev.

Calculation of gravitational wave forms from black hole collisions and disk collapse: Applying perturbation theory to numerical spacetimes

Many simulations of gravitational collapse to black holes become inaccurate before the total emitted gravitational radiation can be determined. The main difficulty is that a significant component of the radiation is still in the near-zone, strong field region at the time the simulation breaks down. We show how to calculate the emitted waveform by matching the numerical simulation to a perturbation solution when the final state of the system approaches a Schwarzschild black hole. We apply the technique to two scenarios: the head-on collision of two black holes, and the collapse of a disk to a black hole. This is the first reasonably accurate calculation of the radiation generated from colliding black holes that form from matter collapse.Comment: 8 pages (RevTex 3.0 with 7 uuencoded figures

S-Duality at the Black Hole Threshold in Gravitational Collapse

We study gravitational collapse of the axion/dilaton field in classical low energy string theory, at the threshold for black hole formation. A new critical solution is derived that is spherically symmetric and continuously self-similar. The universal scaling and echoing behavior discovered by Choptuik in gravitational collapse appear in a somewhat different form. In particular, echoing takes the form of SL(2,R) rotations (cf. S-duality). The collapse leaves behind an outgoing pulse of axion/dilaton radiation, with nearly but not exactly flat spacetime within it.Comment: 8 pages of LaTeX, uses style "revtex"; 1 figure, available in archive, or at ftp://ftp.itp.ucsb.edu/figures/nsf-itp-95-15.ep

The two-phase approximation for black hole collisions: Is it robust?

Recently Abrahams and Cook devised a method of estimating the total radiated energy resulting from collisions of distant black holes by applying Newtonian evolution to the holes up to the point where a common apparent horizon forms around the two black holes and subsequently applying Schwarzschild perturbation techniques . Despite the crudeness of their method, their results for the case of head-on collisions were surprisingly accurate. Here we take advantage of the simple radiated energy formula devised in the close-slow approximation for black hole collisions to test how strongly the Abrahams-Cook result depends on the choice of moment when the method of evolution switches over from Newtonian to general relativistic evolution. We find that their result is robust, not depending strongly on this choice.Comment: 4 pages, 3 figures, submitted to Classical and Quantum Gravit

The collision of boosted black holes

We study the radiation from a collision of black holes with equal and opposite linear momenta. Results are presented from a full numerical relativity treatment and are compared with the results from a ``close-slow'' approximation. The agreement is remarkable, and suggests several insights about the generation of gravitational radiation in black hole collisions.Comment: 8 pages, RevTeX, 3 figures included with eps