The detection of gravitational waves is the most exciting prospect for experimental relativity today. With ground based interferometers such as LIGO, VIRGO and GEO online and the space based LISA project in preparation, the experimental apparatus necessary for such work is steadily taking shape. Yet, however capable these experiments are of taking data, the actual detection of gravitational waves relies in a significant way on making sense of the collected signals. Some of the data analysis techniques already in place use knowledge of expected waveforms to aid the search. This is manifested in template based data analysis techniques. For these techniques to be successful, potential sources of gravitational radiation must be identified and the corresponding waveforms for those sources must be computed. It is in this context that black hole perturbation theory has its most immediate consequences.; This dissertation presents a new framework for black hole perturbation theory based on the spin coefficient formalism of Geroch, Held and Penrose. The two main components of this framework are a new form for the perturbed Einstein equations and a Maple package, GHPtools, for performing the necessary symbolic computation. This framework provides a powerful tool for performing analyses generally applicable to the entire class of Petrov type D solutions, which include the Kerr and Schwarzschild spacetimes.; Several examples of the power and °exibility of the framework are explored. They include a proof of the existence of the radiation gauges of Chrzanowski in Petrov type II spaces as well as a derivation of the Teukolsky-Starobinsky relations that makes no reference to separation of variables. Furthermore, a method of determining the non-radiated multipoles in type D spaces is detailed.
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