Modeling the Dynamics of Black Hole Systems and the Ringdown of Black Hole Spacetimes
Fortunately, by the time Advanced LIGO-Virgo started observing gravitational waves from merging black holes in 2015, theoretical models had already been developed which would greatly contribute to the interpretation of that data. Thanks to numerical relativity, the merger of isolated near-equal mass...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2023
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| Online Access: | https://hdl.handle.net/1721.1/150680 https://orcid.org/0000-0002-0053-9001 |
| Summary: | Fortunately, by the time Advanced LIGO-Virgo started observing gravitational waves from merging black holes in 2015, theoretical models had already been developed which would greatly contribute to the interpretation of that data. Thanks to numerical relativity, the merger of isolated near-equal mass ratio binary black holes, and the gravitational waves they emit, has been well understood. However, to capitalize on future observations made by current and planned detectors, much work will be needed to expand theoretical models towards all kinds of gravitational-wave sources, including binaries with arbitrary mass ratios and spins, and binaries that interact with their astrophysical environments.
This thesis explores how to model a variety of gravitational wave sources using semi-analytic techniques including black hole perturbation theory and post-Newtonian theory. First, we describe work to predict and characterize the ringdown gravitational waves from misaligned binary black hole mergers. Working in the large mass ratio limit, we use Teukolsky's equation to calculate the worldline for plunging bodies with varying orbital geometries. Perturbations about Kerr spacetime are a linear superposition of quasinormal modes, and we calculate the amplitude of these mode frequencies as excited by a plunging body. The key result is that the mode amplitudes can be cleanly mapped from kinematic angles describing the plunge geometry. Next, we use this mapping to construct a ringdown waveform model consisting of quasinormal modes. Using a white Gaussian noise model, we conduct parameter estimation on the ringdown waveform and demonstrate how the mode amplitudes can be measured. Finally, we investigate the post-Newtonian orbital dynamics of hierarchical black hole triples. We find that for certain triple systems, when the tertiary is much more massive than the inner binary, post-Newtonian three-body resonances can substantially modify the orbital evolution. |
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