Wave extraction in numerical evolutions of distorted black holes

The study of black holes and their interactions and the extraction of gravitational waves become of primary importance from both - the astrophysical and theoretical points of view now that the first gravitational detectors have started operating; gravitational waves, while certainly extremely weak, are also extremely pervasive and thus a novel and very promising way of exploring the universe. Space-times containing highly distorted black holes will generally have strong time-dependent gravitational fields and presumably provide the strongest sources of gravitational waves in the universe. This work focuses on two fundamental problems in modern numerical relativity: (1) Creating valid initial data of non-perturbative distorted black hole space-times for numerical evolution, and (2) extracting the radiation quantities in a coordinate independent way, using the Newman-Penrose formalism. I first consider the initial data for such distorted black hole space-times, prescribing them successfully in a simplified situation of superimposed time symmetric Brill waves, and leading the way to more general initial data which corresponds to rotating black holes. To drop the assumption of time symmetric initial hypersurfaces will be subject of future work. Next I move to the numerical evolution and introduce a simple but stable way to perform excision in spherical coordinates. Finally, I extract the gravitational wave signal from the numerical simulations, using the Newman-Penrose formalism, in particular the Weyl scalars. I adopt a particular frame where the Weyl scalars acquire physical meaning, and can be directly associated with the waveform. Moreover, I derive a formula to calculate the energy carried away by the wave. Comparison of the even and odd parity waveforms of our non-perturbation approach with the metric perturbation approaches such as Regge-Wheeler [1], Zerilli [2] and Teukolsky [3] will partly be discussed and partly be subject of future work