Mijan Huq

Initial data and coordinates for multiple black hole systems

We present here an alternative approach to data setting for spacetimes with multiple moving black holes generalizing the Kerr-Schild form for rotating or non-rotating single black holes to multiple moving holes. Because this scheme preserves the Kerr-Schild form near the holes, it selects out the behaviour of null rays near the holes, may simplify horizon tracking, and may prove useful in computational applications. For computational evolution, a discussion of coordinates (lapse function and shift vector) is given which preserves some of the properties of the single-hole Kerr-Schild form.

Approximate analytical solutions to the initial data problem of black hole binary systems

We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these initial data solutions makes them easier to implement in numerical evolutions than the traditional numerical approach of solving the elliptic equations derived from the Einstein constraints. Although in general the problem of setting up initial conditions for black hole binary simulations is complicated by the presence of singularities, we show that the methods presented in this work provide initial data with l 1 and l ‘ norms of violation of the constraint equations falling below those of the truncation error ~residual error due to discretization! present in finite difference codes for the range of grid resolutions currently used. Thus, these data sets are suitable for use in evolution codes. Detailed results are presented for the case of a head-on collision of two equal-mass M black holes with specific angular momentum 0.5M at an initial separation of 10M. A straightforward superposition method yields data adequate for resolutions of h5M/4, and an ‘‘attenuated’’ superposition yields data usable to resolutions at least as fine as h5M/8. In addition, the attenuated approximate data may be more tractable in a full ~computational! exact solution to the initial value problem.

Locating boosted Kerr and Schwarzschild apparent horizons

We describe a finite-difference method for locating apparent horizons in generic spacetimes and illustrate its capabilities on boosted Kerr and Schwarzschild black holes. Our model spacetime is given by the Kerr-Schild metric. We apply a Lorentz boost to this spacetime metric and then carry out a 311 decomposition. The result is a slicing of Kerr-Schwarzschild spacetime in which the black hole is propagated and Lorentz contracted. We show that our method can locate distorted apparent horizons efficiently and accurately.

Three-dimensional adaptive evolution of gravitational waves in numerical relativity

Adaptive techniques are crucial for successful numerical modeling of gravitational waves from astrophysical sources such as coalescing compact binaries, since the radiation typically has wavelengths much larger than the scale of the sources. We have carried out an important step toward this goal: the evolution of weak gravitational waves using adaptive mesh refinement in the Einstein equations. The 2-level adaptive simulation is compared with unigrid runs at coarse and fine resolution, and is shown to track closely the features of the fine grid run.

Toward gravitational wave detection

An overview of some tools and techniques being developed for data conditioning (regression of instrumental and environmental artifacts from the data channel), detector design evaluation (modeling the science “reach” of alternative detector designs and configurations), noise simulations for mock data challenges and analysis system validation, and analyses for the detection of gravitational radiation from gamma-ray burst sources.

Analysis of 'gauge modes' in linearized relativity

By writing the complete set of 3 + 1 (ADM) equations for linearized waves, we are able to demonstrate the properties of the initial data and of the evolution of a wave problem set by Alcubierre and Schutz. We show that the gauge modes and constraint error modes arise in a straightforward way in the analysis, and are of a form which will be controlled in any well specified convergent computational discretization of the differential equations.