Accurate Gravitational Waveforms from Binary Black-hole Systems

Citation

Boyle, Michael (2009) Accurate Gravitational Waveforms from Binary Black-hole Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/7NSM-RW43. https://resolver.caltech.edu/CaltechETD:etd-01122009-143851

Abstract

We examine various topics involved in the creation of accurate theoretical gravitational waveforms from binary black-hole systems.

In Chapter 2 a pseudospectral numerical code is applied to a set of analytic or near-analytic solutions to Einstein's equations which comprise a testbed for numerical-relativity codes. We then discuss methods for extracting gravitational-wave data from numerical simulations of black-hole binary systems, and introduce a practical technique for obtaining the asymptotic form of that data from finite simulation domains in Chapter 3. A formula is also developed to estimate the size of near-field effects from a compact binary. In Chapter 4 the extrapolated data is then compared to post-Newtonian (PN) approximations. We compare the phase and amplitude of the numerical waveform to a collection of Taylor approximants, cross-validating the numerical and PN waveforms, and investigating the regime of validity of the PN waveforms. Chapter 5 extends that comparison to include Padé and effective-one-body models, and investigates components of the PN models. In each case, a careful accounting is made of errors. Finally, we construct a long post-Newtonian–numerical hybrid waveform and evaluate the performance of LIGO's current data-analysis methods with it. We suggest certain optimizations of those methods, including extending the range of template mass ratios to unphysical ranges for certain values of the total mass, and a simple analytic cutoff frequency for the templates which results in nearly optimal matches for both Initial and Advanced LIGO.

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