Computational Methods for Gravitational Wave Physics: Spectral Cauchy-Characteristic Extraction and Tidal Splicing

As the aLIGO and Virgo detectors continue to improve their sensitivity for observing gravitational waves from merging compact binaries, they will require ever more precise theoretical predictions to extract a detailed understanding of the physics governing these merging systems. This thesis discusses advancements within computing the gravitational waveforms along two avenues of research: the continued development of a spectral Cauchy-Characteristic Extraction (CCE) code and the presentation of a novel method called 'Tidal Splicing' for generating waveforms for binary neutron star (BNS), black hole-neutron star (BHNS), and even Beyond GR systems. Due to the finite extents of typical 3+1 simulations of merging binaries, the waveforms they generate can suffer from near-zone effects and lingering gauge ambiguities. CCE was developed in order evolve radiating gravitational waves as they propagate outward to future null infinity, allowing studies connecting the dynamical spacetime of binary evolutions to effects seen by distant observers, such as superkicks, and angluar and linear momentum fluxes. A recent spectral version of CCE showed promising improvements in accuracy and efficiency over the older finite-differencing code, PittNull. However, lingering issues with the numerics and implementation of the theory prevented it from wide spread use. We detail the developments updated its initial release and demonstrate the enhancement in accuracy they yield beyond the capabilities of PittNull. The method of Tidal Splicing enhances the inexpensive Post-Newtonian (PN) tidal corrections with BBH waveforms from numerical simulations to generate waveforms corresponding to inpsiraling BNS or BHNS systems. This leverages the accuracy of numerical BBH waveforms to effectively replace the corresponding unknown PN terms. In addition, by picking individual terms in the PN tidal expansions to include, then comparing with existing numerical simulations, we are able to probe the significance of each contribution to the total difference in evolution between BBH and BNS or BHNS inspirals. We also demonstrate how the splicing concepts used for tidal effects can extended in order to model waveforms with corrections according to theories beyond GR using an example case of a resonating ultra-compact object.